ClipArt ETC
Illustration used to prove the theorem, "Two angles whose sides are parallel, each to each, are either equal or supplementary."

2 Angles With Parallel Sides Theorem

Illustration used to prove the theorem, "Two angles whose sides are parallel, each to each, are either…

Illustration used to prove the theorem, "Two angles whose sides are perpendicular, each to each, are either equal or supplementary."

2 Angles With Perpendicular Sides Theorem

Illustration used to prove the theorem, "Two angles whose sides are perpendicular, each to each, are…

Illustration used to prove the theorem, "The sum of the angles of any triangle is two right angles."

Sum Of Angles In Triangle Theorem

Illustration used to prove the theorem, "The sum of the angles of any triangle is two right angles."

Illustrations used to construct an ellipse. Fig. 59 shows a compass at C used to strike a circle. Where the circle intersects the line at D and B, place pins. These pins represent the foci of the ellipse. Use a cord and a pencil to draw the ellipse as shown in figure 60. This illustrates the definition of an ellipse.

Construction Of An Ellipse

Illustrations used to construct an ellipse. Fig. 59 shows a compass at C used to strike a circle. Where…

"Diagram of head and brain of human foetus six weeks old (heavy boundaries). The dotted line indicates the outline of the brain of a foetus three months old. Note thee great growth of the hemisphere (h). cer, cerebellum; med, medulla oblongata; mes, mesencephalon; p, pituitary body; pr, prosencephalon; s.c., spinal cord; th, thalamencephalon; 1, olfactory nerve; 2, optic nerve." -Galloway, 1915

Human Fetus

"Diagram of head and brain of human foetus six weeks old (heavy boundaries). The dotted line indicates…

"In the triangle above, the line AB is its altitude. Since we know how to find the area of one triangle, we can find the areas of as many triangles as we have made from our circle. Therefore, to find the area of a circle: Find the area of one of the triangles and multiply by the number of triangles." -Foster, 1921

Area of Circle with Triangles

"In the triangle above, the line AB is its altitude. Since we know how to find the area of one triangle,…

An illustration showing the construction used to divide a line AB into two equal parts; and to erect a perpendicular through the middle. "With the end A and B as centers, draw the dotted circle arcs with a radius greater than half the line. Through the crossings of the arcs draw the perpendicular CD, which divides the line into two equal parts."

Construction Of A Line Divided In Equal Parts

An illustration showing the construction used to divide a line AB into two equal parts; and to erect…

An illustration showing the construction used to erect a perpendicular from a point to a line. "With C as a center, draw the dotted circle arc so that it cuts the line at A and B. With A and B as centers, draw the dotted cross arcs at D with equal radii. Draw the required perpendicular through C and crossing D."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular from a point to a line. "With…

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the point D as a center at a distance from the line, and with AD as radius, draw the dotted circle arc so that it cuts the line at E through E and D, draw the diameter EC: then join C and A, which will be the required perpendicular."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the…

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the dotted arc ED, with E as a center, draw through C the dotted arc F.C. With the radius FC and E as a center, draw the cross arc at D. Join C with the cross at D, which will be the required parallel line.

Construction Of A Parallel

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the…

An illustration showing the construction used to erect a parallelogram given two sides and an angle. "Draw the base line DE, and make the angle FDE = C; lines DE = B and DF = A; complete the parallelogram by cross arcs at G, and the problem is thus solved."

Construction Of A Parallelogram

An illustration showing the construction used to erect a parallelogram given two sides and an angle.…

An illustration showing the construction used to divide the line AB in the same proportion of parts as AC. "Join C and B, and through the given divisions 1, 2, and 3 draw lines parallel with CB, which solves the problem."

Divide A Line Proportionately

An illustration showing the construction used to divide the line AB in the same proportion of parts…

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B as centers, draw the circle arcs AED and BEC. Divide the arc BE in two equal parts at F, and with EF as radius and E as center, draw the circle CFD. Join A and CB and D, C and D, which completes the required square."

Square Constructed Upon A Given Line

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B…

An illustration showing how to construct a tangent to a circle through a given point in a circumference. "Through a given point A and center C, draw the line BC. With A as a center, draw the circle arcs B and C; with B and C as centers, draw the cross arcs D and E; then join D and E, which is the required tangent."

Construction Of Tangent To Circle

An illustration showing how to construct a tangent to a circle through a given point in a circumference.…

An illustration showing how to construct a tangent circle to 2 given circles. "Join centers C and c of the given circles, and extend the line to D; draw the radii AC and ac parallel with one another. Join Aa, and extend the line to D. On CD as a diameter, draw the half circle CeD; on cD as a diameter, draw the half circle cfD; then the crossings e and f are tangenting points of the circles."

Construction Of Circle Tangent To 2 Circles

An illustration showing how to construct a tangent circle to 2 given circles. "Join centers C and c…

He was a mathematician, geographer, astronomer, and astrologer. "The name of a line Graeco-Egyptain kings, who succeeded on the division of the empire of Alexander the Great, to the portion of his dominions of which Egypt was the head." -Marshall

Ptolemy in Profile

He was a mathematician, geographer, astronomer, and astrologer. "The name of a line Graeco-Egyptain…

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join the centers C and c of the given circles, and extend the line to D; draw the radii AC and ac parallel with one another. Join Aa, and extend the line to D. On CD as a diameter, draw the half circle CeD; on cD as a diameter, draw the half circle cfD; then the crossings e and f are the tangenting points of the circles."

Construction Of Tangent To 2 Circles

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join…

An illustration showing how to construct a tangent between 2 given circles. "Join the centers C and c of the given circles; draw the dotted circle arcs, and join the crossing m, n, which line cuts the center line at a. With aC as diameter, draw the half circle afC; and with ac as a diameter, draw the half circle cea; then the crossings e and f are the tangenting points of the circles."

Construction Of Tangent Between 2 Circles

An illustration showing how to construct a tangent between 2 given circles. "Join the centers C and…

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the given radius r to the radius R of the circle, and draw the arc cd. Draw the line ce parallel with and at a distance r from the line AB. Then the crossing c is the center of the required circle that will tangent the given line and circle."

Construction Of A Circle Tangent To A Line And A Circle

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle. "Through the given point C, draw the tangent GF; bisect the angle FGE; then o is the center of the required circle that will tangent AB at C, and the line DE."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "Through the given point C, draw the line EF at right angles to AB; set off from C the radius r of the given circle. Join G and F. With G and F as centers draw the arc crosses m and n. Join mn, and where it crosses the line EF is the center of the required circle."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "From C, erect the perpendicular CG; set off the given radius r from C to H. With H as a center and r as radius, draw the cross arcs on the circle. Through the cross arcs draw the line IG; then G is the center of the circle arc FIC, which tangents the line at C and the circle at F."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw the center line AB between the given lines; assume D to be the tangenting point of the circles; draw DC at right angles to AB. With C as center and CD as radius, draw the circle EDF. From E, draw Em at right angles to EF; and from F draw Fm at right angles to FE; then m and n are the centers for the required circles."

Construction Of Two Circles That Tangent Themselves and 2 Given Lines

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw…

An illustration showing how to construct a circle that tangents two given lines inclined to one another with the one tangenting point being given. "Draw the center line GF. From E, draw EF at right angles to AB; then F is the center of the circle required.

Construction Of A Circle That Tangents 2 Given Lines

An illustration showing how to construct a circle that tangents two given lines inclined to one another…

An illustration showing how to construct a circle that tangents two given lines and goes through a given point c on the line FC, which bisects the angle of the lines. "Through C draw AB at right angles to CF; bisect the angles DAB and EBA, and the crossing on CF is the center of the required circle."

Construction Of A Circle That Tangents 2 Given Lines And Goes Through A Given Point

An illustration showing how to construct a circle that tangents two given lines and goes through a given…

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and from the center C erect the perpendicular CD. Bisect the radius AC at E; with E as center, and DE as radius, draw the arc DE, and the straight line DF is the length of the side of the pentagon."

Construction Of A Pentagon Inscribed In A Circle

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and…

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular to and half the length of AB; join A and C prolonged to D; with C as center and CB as radius, draw the arc BD; then the chord BB is the radius of the circle circumscribing the pentagon. With A and B as centers, and BD as radius, draw the cross O in the center."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular…

An illustration showing how to construct a pentagon on a given line without resort to its center. "From B erect Bo perpendicular to and equal to AB; with C as center and Co as radius, draw the arc Do, then AD is the diagonal of the pentagon. With AD as radius and A as center, draw the arc DE; and with E as center and AB as radius, finish the cross E, and thus complete the pentagon."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line without resort to its center. "From…

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center and AB as radius, draw the circle AFDEC; from B, draw BI at right angles to AB; divide the angles ABC and DBC each into two equal parts; then BD is one side of the octagon. With A and E as centers, draw the arcs HKE and AKI, which determine the points H and I, and thus complete the octagon as shown in the illustration."

Construction Of An Octagon

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center…

An illustration showing how to construct a regular polygon on a given line without resort to its center. "Extend AB to C and, with B as center, draw the half circle ADB. Divide the half circle into as many parts as the number of sides in the polygon, and complete the construction as shown on the illustration."

Construction Of A Regular Polygon On A Line

An illustration showing how to construct a regular polygon on a given line without resort to its center.…

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide OA and OB each into three equal parts; draw the quadrant AC. From C, draw the line Cc through the point 1. Through the points 2 draw de at an angle of 45° with the major axis. Then 2 is the center for the ends of the ellipse; e is the center for the arc dc; and C is the center for the arc cf."

Construction Of An Isometric Ellipse

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide…

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the shaft, and C1, 2, 3, et., is the center line of the shaft. From o, set off the small distance oa; and set off a1 - R. Set off the same small distance from a to b, and make b2 = R. Continue in the same way with the other points, and the anti-friction curve is thus constructed.

Construction Of Shield's Anti-friction Curve

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the…

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles with diameters equal to the long and short axes of the desired ellipse. Draw from o any number of radii, A, B, etc. Draw a line Bb' parallel to n and bb' parallel to m, then b is a point in the desired ellipse.

Construction Of An Ellipse

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles…

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle and base line C into a number of equal parts, draw through the division point the ordinates and abscissas, make aa' = 1d, bb' = 2'e, cc = 3f, then ab' and c' are points in the cycloid. In the Epicycloid and Hypocycloid the abscissas are circles and the ordinates are radii to one common center."

Construction Of A Cycloid

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle…

An illustration showing a quadrilateral inscribed in a circle that is tangent to a line.

Quadrilateral Inscribed In A Circle

An illustration showing a quadrilateral inscribed in a circle that is tangent to a line.

An illustration showing a triangle with angles A, C, and D inscribed in a circle which is tangent to a line.

Triangle Inscribed In A Circle

An illustration showing a triangle with angles A, C, and D inscribed in a circle which is tangent to…

This chart of comparisons can be used with the following questions: "Which line is twice B? Which two added make H? Which line is the difference between F and D? Call A 5; name the others. Call A 6, and name the others." -Foster, 1921

Comparisons Chart

This chart of comparisons can be used with the following questions: "Which line is twice B? Which two…

Diagram of a soccer field.

Soccer Field

Diagram of a soccer field.

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant that illustrates the following geometric relationship: a:t = t:b, t&sup2 = ab

Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with an exterior angle formed between a tangent and a secant…

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates the following geometric relationship: t&sup2 = (a + b)(a - b).

Model Of Geometric Relationships In A Circle

An illustration showing a model of a circle with angles formed between tangents and secants that illustrates…

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates the following geometric relationship: "x = aR/(R - r), a = √(t&sup2 + (R - r)&sup2), t = √(a&sup2 - (R - r)&sup2, sin.v = t/a."

Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates the following geometric relationship: " t = √(a&sup2 - (R + r)&sup2, a = √(t&sup2 - (R + r)&sup2 "

Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

Illustration used to resolve a motion into two components, one of which is perpendicular, and the other parallel, to a given line, as ef. Vector ad represents the motion; ab = ad cos(dab), the component parallel to ef; and ac = ad sin(dab), the components perpendicular to ef.

Vector Motion Into Two Components - Resultant

Illustration used to resolve a motion into two components, one of which is perpendicular, and the other…

Illustration for rigidly-connected points. "If two points are so connected that their distance apart is invariable and if their velocities are resolved into components at right angles to and along the straight line connecting them, the components along this line of connection must be equal, otherwise the distance between the points would change."

Velocities Of Rigidly-connected Points

Illustration for rigidly-connected points. "If two points are so connected that their distance apart…

Illustration for rigidly-connected points. In the series of links shown, c and d are fixed axes and f slides on the line ff<sub>1</sub>.

Velocities Of Rigidly-connected Points

Illustration for rigidly-connected points. In the series of links shown, c and d are fixed axes and…

A diagram of an annulosa showing its external skeleton made up of segments or rings arranged along a longitudinal line, and consisting mostly of hardened skin. Labels: 1, vascular system,; 2, digestive organs; 3, ganglia.

Diagram of an Annulosa

A diagram of an annulosa showing its external skeleton made up of segments or rings arranged along a…

In birds the muscles system is remarkable for their marked line of attachment to their tendons. Labels: 1, Occipito-Frontalis. 2, Orbicularis Palpaebrarum. 3, Temporal. 4, Masseter. 5, Sterno-cleido-Mastoid. 6, Trapezius. 7, Latissimus Dorsi. 8, Pectoralis. 9, Deltoid. 10, Biceps. 11, Triceps. 12, Gluteii. 13, Levator Caudae. 14, Rectus Femoris. 15, Gastrocnemius muscle.

The Superficial Muscles of a Hawk

In birds the muscles system is remarkable for their marked line of attachment to their tendons. Labels:…

A side view of the chest and abdomen in respiration. Labels: 1, The cavity of the chest. 2, The cavity of the abdomen. 3, The line of direction for the diaphragm when relaxed in expiration. 4, The line of direction for the diaphragm when contracted in inspiration. 5, 6, The position of the front walls of the chest and abdomen in inspiration. 7, 8, The position of the front walls of the abdomen and chest in expiration.

A Side View of the Chest and Abdomen in Respiration

A side view of the chest and abdomen in respiration. Labels: 1, The cavity of the chest. 2, The cavity…

"Generalized columnar section, northern Black Hills." -Walcott, 1901

Strata Thickness

"Generalized columnar section, northern Black Hills." -Walcott, 1901

"Effect of removal of a leaflet from a palmately compound leaf (e.g. Woodbine). B, normal leaf; C, after removal of upper right-hand leaflet. A, Unbroken lines represent average normal position of leaflets; dotted lines, average position of leaflets after operation; barred line, position of leaflet removed." -Gager, 1916

Leaflet Removal

"Effect of removal of a leaflet from a palmately compound leaf (e.g. Woodbine). B, normal leaf; C, after…

Vertical section of a molar tooth. Labels: a, enamel of the crown, the line of which indicate the arrangement of its columns; b, dentine; c,cement; d, pulp cavity.

Vertical Section of a Molar

Vertical section of a molar tooth. Labels: a, enamel of the crown, the line of which indicate the arrangement…

Diagram of the appearance in fresh muscle fiber. Labels: A, At low focus (B) the muscle columns appear dark and in a line with the granules, sarcoplasm light. At high focus (A) the sarcoplasm is dark, muscle columns light, and two rows of granules appear in a line with the sarcoplasm and alternating with the muscle columns.

Muscle Fiber

Diagram of the appearance in fresh muscle fiber. Labels: A, At low focus (B) the muscle columns appear…

Section of the aorta, to show the action of the semilunar valve. A is intended to show the valves, represented by the dotted lines, lying near the arterial walls, represented by the continuous outer line. B (after Hunter) shows the arterial wall distended into three pouched (a), and drawn away from the valves, which are straightened into the form of an equilateral triangle, as represented by the dotted line.

Action of Semilunar Valve

Section of the aorta, to show the action of the semilunar valve. A is intended to show the valves, represented…

The axes of rotation of rib movement is two; one corresponding with a line drawn through two articulations which the ribs forms with the spine (a, b); and the other with a line drawn from one of these (head of rib) to the sternum (A, B); the motion of the rib around the latter axis being somewhat after the fashion of raising the handle of a bucket.

Movement of Ribs

The axes of rotation of rib movement is two; one corresponding with a line drawn through two articulations…

Dorsal or posterior view of the medulla, fourth ventricle, and mesencephalon. Labels: p.n., line of the posterior roots of the spinal nerves; p.m.f., posterior median fissure; f.g., funiculus gracilis; cl., its clava; f.c., funiculus cuneatus; f.R., funiculus of Rolando; r.b., restiform body; c.s., calamus scriptorius; l, section of ligula or taenia; part of choroid plexus is seen beneath t; l.r., lateral recess of the ventricle; str., striae acusticae; i.f., inferior fossa; s.f., posterior fossa; between it and the median sulcus is the fasciculus teres; cbl., cut surface of the cerebellar hemisphere; nd., central or gray matter; s.m.v., superior medullary velum; lng., ligula; s.c.p., superior cerebellar peduncle cut longitudinally; cr., combined section of the three cerebellar peduncles; c.q.s., c.q.i., corpora quadrigemina (superior and inferior); fr., fraenulum; f; f., fibers of the fillet seen on the surface of the tegmentum; c, crusti; l.g., lateral groove; c.g.i, corpus geniculum internus; th., posterior part of the thalamus; p., pineal body. The Roman numbers indicate the corresponding cranial nerves.

Medulla

Dorsal or posterior view of the medulla, fourth ventricle, and mesencephalon. Labels: p.n., line of…

Longitudinal and vertical diagrammatic section of a vertebrate brain. Mb, midbrain: what lies in front of this is the fore-, and what lies behind, the hindbrain; Lt, lamina terminalis; Olf, olfactory lobes; Hmp, hemispheres; Th. E, thalamencephalon; Pn, pineal gland; Py, pituitary body; F. M., foramen of Munro; cs, corpus striatum; Th, optic thalamus; CC, crura cerebri; the mass lying above the canal represents the corpora quadrigemina; Cb, cerebellum; I-IX, the nine pairs of cranial nerves; 1, olfactory ventricle; 2, lateral ventricle; 3, third ventricle; 4, fourth ventricle; +, iter a tertio ad quartum ventriculum. Lamina terminalis is represented by the strong black line joining Pn and Py.

Vertical Section of a Vertebrate Brain

Longitudinal and vertical diagrammatic section of a vertebrate brain. Mb, midbrain: what lies in front…

Brain of dog, viewed from above and in profile. F, frontal fissure sometimes termed crucial sulcus, corresponding to the fissure of Rolando in man. S, fissure of Sylvius, around which the four longitudinal convolutions are concentrically arranged; 1, flexion of head on the neck, in the median line; 2, flexion of head on the anterior limb; 5, 6, flexion and extension of posterior limb; 7, 8, 9, contraction of orbicularis oculi, and the facial muscles in general. The unshaded part in that exposed by the opening of the skull.

Brain of a Dog

Brain of dog, viewed from above and in profile. F, frontal fissure sometimes termed crucial sulcus,…

Embryo chick (36 hours), viewed from beneath as a transparent object (magnified). Labels:pl, outline of pellucid area; FB, forebrain, or first cerebral vesicle: from its sides project op, the optic vesicles; SO, backward limit of somatopleure fold, "tucked in", under head; A, head-fold of true amnion; a', reflected layer of amnion, sometimes termed "false amnion;" sp, backward limit of splanchnopleure folds, along which run the omphalomesaraic veins uniting to form h, the heart, which is continued forwards into ba, the bulbus arteriosus; d, the foregut, lying behind the heart, and having a wide crescentic opening between the splanchnopleure folds; HB, hindbrain; MB, midbrain; pv, protovertebrae lying behind the foregut; mc, line of junction of medullary folds and of notochord; ch, front end of notochord; vpl, vertebral plated; pr, the primitive groove at its caudal end.

Embryo Chick

Embryo chick (36 hours), viewed from beneath as a transparent object (magnified). Labels:pl, outline…

Diagram of part of digestive tract of a chick (4th day). The black line represents hypoblast , the outer shading mesoblast; lg, lung diverticulum with expanded end forming primary lung vesicles; St, stomach; l, two hepatic diverticulum, with their terminations united by solid rows of hypoblast cells; p, diverticulum of the pancreas with the vesicular diverticula coming from it.

Digestive Tract of a Chick

Diagram of part of digestive tract of a chick (4th day). The black line represents hypoblast , the outer…

"The Watered Pecten belongs to the scallop-shells. The shell is generally nearly circular, more or less elongated, and terminated toward the summit in a straight line."

Pecten Pseudamussium (Chenu.)

"The Watered Pecten belongs to the scallop-shells. The shell is generally nearly circular, more or less…