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Illustration showing coterminal angles of 180° and -180°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

180° and -180° Coterminal Angles

Illustration showing coterminal angles of 180° and -180°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 185° and -175°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

185° and -175° Coterminal Angles

Illustration showing coterminal angles of 185° and -175°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 190° and -170°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

190° and -170° Coterminal Angles

Illustration showing coterminal angles of 190° and -170°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 195° and -165°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

195° and -165° Coterminal Angles

Illustration showing coterminal angles of 195° and -165°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 200° and -160°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

200° and -160° Coterminal Angles

Illustration showing coterminal angles of 200° and -160°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 205° and -155°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

205° and -155° Coterminal Angles

Illustration showing coterminal angles of 205° and -155°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 210° and -150°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

210° and -150° Coterminal Angles

Illustration showing coterminal angles of 210° and -150°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 215° and -145°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

215° and -145° Coterminal Angles

Illustration showing coterminal angles of 215° and -145°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 220° and -140°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

220° and -140° Coterminal Angles

Illustration showing coterminal angles of 220° and -140°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 225° and -135°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

225° and -135° Coterminal Angles

Illustration showing coterminal angles of 225° and -135°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 230° and -130°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

230° and -130° Coterminal Angles

Illustration showing coterminal angles of 230° and -130°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 235° and -125°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

235° and -125° Coterminal Angles

Illustration showing coterminal angles of 235° and -125°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 240° and -120°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

240° and -120° Coterminal Angles

Illustration showing coterminal angles of 240° and -120°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 245° and -115°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

245° and -115° Coterminal Angles

Illustration showing coterminal angles of 245° and -115°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 250° and -110°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

250° and -110° Coterminal Angles

Illustration showing coterminal angles of 250° and -110°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 255° and -105°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

255° and -105° Coterminal Angles

Illustration showing coterminal angles of 255° and -105°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 260° and -100°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

260° and -100° Coterminal Angles

Illustration showing coterminal angles of 260° and -100°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 265° and -95°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

265° and -95° Coterminal Angles

Illustration showing coterminal angles of 265° and -95°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 270° and -90°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

270° and -90° Coterminal Angles

Illustration showing coterminal angles of 270° and -90°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 275° and -85°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

275° and -85° Coterminal Angles

Illustration showing coterminal angles of 275° and -85°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 280° and -80°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

280° and -80° Coterminal Angles

Illustration showing coterminal angles of 280° and -80°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 285° and -75°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

285° and -75° Coterminal Angles

Illustration showing coterminal angles of 285° and -75°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 290° and -70°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

290° and -70° Coterminal Angles

Illustration showing coterminal angles of 290° and -70°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 295° and -65°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

295° and -65° Coterminal Angles

Illustration showing coterminal angles of 295° and -65°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 300° and -60°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

300° and -60° Coterminal Angles

Illustration showing coterminal angles of 300° and -60°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 305° and -55°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

305° and -55° Coterminal Angles

Illustration showing coterminal angles of 305° and -55°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 310° and -50°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

310° and -50° Coterminal Angles

Illustration showing coterminal angles of 310° and -50°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 315° and -45°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

315° and -45° Coterminal Angles

Illustration showing coterminal angles of 315° and -45°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 320° and -40°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

320° and -40° Coterminal Angles

Illustration showing coterminal angles of 320° and -40°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 325° and -35°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

325° and -35° Coterminal Angles

Illustration showing coterminal angles of 325° and -35°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 330° and -30°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

330° and -30° Coterminal Angles

Illustration showing coterminal angles of 330° and -30°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 335° and -25°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

335° and -25° Coterminal Angles

Illustration showing coterminal angles of 335° and -25°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 340° and -20°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

340° and -20° Coterminal Angles

Illustration showing coterminal angles of 340° and -20°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 345° and -15°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

345° and -15° Coterminal Angles

Illustration showing coterminal angles of 345° and -15°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 350° and -10°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

350° and -10° Coterminal Angles

Illustration showing coterminal angles of 350° and -10°. Coterminal angles are angles drawn…

Illustration showing coterminal angles of 355° and -5°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

355° and -5° Coterminal Angles

Illustration showing coterminal angles of 355° and -5°. Coterminal angles are angles drawn in…

Illustration showing coterminal angles of 360° and 0°. Coterminal angles are angles drawn in standard position that have a common terminal side. In this illustration, only the positive angle is labeled with the proper degree measure.

360° and 0° Coterminal Angles

Illustration showing coterminal angles of 360° and 0°. Coterminal angles are angles drawn in…

Half of the lower jaw. Labels: a, the base; b, the angle; c, the ramus; d, the condyle; e, the coronaid process; h, the two incisors or cutting teeth; i, one canine; k, two small molar; l, three large molar or grinding teeth.

Lower Jaw

Half of the lower jaw. Labels: a, the base; b, the angle; c, the ramus; d, the condyle; e, the coronaid…

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is greater than either of the remote interior angles."

Exterior Angle of Triangle Theorem

Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is…

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less side."

Sides of Triangle Theorem

Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, then the angle opposite the third side of the first is greater than the angle opposite the third side of the second."

2 Triangles Theorem

Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…

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."

"Axillary.--Placed in the axilla (arm-pit). A term by which the angle formed by the union of the leaf and the stem is designated." -Newman, 1850

Axillary

"Axillary.--Placed in the axilla (arm-pit). A term by which the angle formed by the union of the leaf…

"Details of a castle: 1. Fortified approach 2. Drawbridge 3. Moat 4. Donjon or keep 5. Towers flanking main entrance 6. Angle towers for defense of outer wall 7. Chapel." -Foster, 1921

Castle Parts

"Details of a castle: 1. Fortified approach 2. Drawbridge 3. Moat 4. Donjon or keep 5. Towers flanking…

"The plant tillers like wheat, but not to the same degree. The cane ground is kept clean by hand-hoeing, or by the plough." -Lupton

Gathering, Sugar Cane

"The plant tillers like wheat, but not to the same degree. The cane ground is kept clean by hand-hoeing,…

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the dotted arc CE: and with the same radius and B as a center, draw the arc GF; then make GF equal to CE; then join BF, which will form the required angle, FBG=CDE."

Construction Of An Equal Angle

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the…

An illustration showing the construction used to divide an angle into two equal parts. "With C as a center, draw the dotted arc DE; with D and E as centers, draw the cross arcs at F with equal radii. Join CF, which divides the angle into the required parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts. "With C as a…

An illustration showing the construction used to divide an angle into two equal parts when the lines do not extend to a meeting point. "Draw the lined CD and CE parallel, and at equal distances from the lines AB and FG. With C as a center, draw the dotted arc BG; and with B and G as centers, draw the cross arcs H. Join CD, which divides the angle into the required equal parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts when the lines…

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 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 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 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…

A detached triangular work in fortification, with two embankments which form a projecting angle. In the figure B B is the ravelin with A its redout, and CC its ditch, DD being the main ditch of the fortress,and E the passage giving access from the fortress to the ravelin.

Ravelin

A detached triangular work in fortification, with two embankments which form a projecting angle. In…

In field fortification, the simplest kind of work employed, consisting of two parapets of earth raised so as to form a salient angle, with the apex towards the enemy and unprotected on the rear. Several redans connected by curtains form lines of intrenchment.

Redans

In field fortification, the simplest kind of work employed, consisting of two parapets of earth raised…

An illustration showing how to use isometric perspective. "This kind of perspective admits of scale measurements the same as any ordinary drawing, and gives a clear representation of the object. It is easily learned. All horizontal rectangular lines are drawn at an angle of 30°. All circles are ellipses of proportion, as shown."

Construction Using Isometric Perspective

An illustration showing how to use isometric perspective. "This kind of perspective admits of scale…

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a semicircle on AB, draw ordinates in the circle at right angle to AB, the corresponding and equal ordinates for the ellipse to be drawn parallel to the lines, and thus the elliptic curve is obtained as shown by the figure."

Construction Of An Ellipse Tangent To Two Parallel Lines

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a…

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and radius r. Divide the angle v into a number of equal parts, draw the radii and tangents for each part, divide the pitch p into an equal number of equal parts, then the first tangent will be one part, second two parts, third three parts, etc., and so the Evolute is traced."

Construction Of An Evolute Of A Circle

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and…

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw AB at right angle to x, and BP parallel to x, divide AB and BP into an equal number of equal parts. From the vertex A draw lines to the divisions on BP, from the divisions on AB draw the ordinates parallel to x, the corresponding intersections are points in the parabola."

Construction Of A Parabola

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw…

An illustration showing how to construct a parabola. "Given the axis of ordinate B, and vertex A. Take A as a center and describe a semicircle from B which gives the focus of the parabola at f. Draw any ordinate y at right angle to the abscissa Ax, take a as radius and the focus f as a center, then intersect the ordinate y, by a circle-arc in P which will be a point in the parabola. In the same manner the whole Parabola is constructed."

Construction Of A Parabola

An illustration showing how to construct a parabola. "Given the axis of ordinate B, and vertex A. Take…