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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."

"A circle may be considered as made up of triangles whose bases form the circumference, and whose altitude is the radius (1/2 diameter) of the circle." This is clearly shown by the cut at the left.

Circle Made Up Of Triangles

"A circle may be considered as made up of triangles whose bases form the circumference, and whose altitude…

A triangular stem.

Triangular Stem

A triangular stem.

A triangular leaf.

Triangular Leaf

A triangular leaf.

A trowel-shaped leaf.

Trowel-Shaped Leaf

A trowel-shaped leaf.

"A slowly grown twig of cherry, three inches long and about ten years old. The pointed bud, l, is a leaf-bud; the more obtuse accessory buds, f, f, are flower-buds." -Bergen, 1896

Cherry Twig

"A slowly grown twig of cherry, three inches long and about ten years old. The pointed bud, l, is a…

"Tips of leaves. a, acuminate or taper-pointed; b, acute; c, obtuse; d, truncate; e, retuse; f, emarginate or notched; g (end leaflet), obcordate; h, cuspidate, - the point sharp and rigid; i, mucronate, - the point merely a prolongation of the midrib." -Bergen, 1896

Leaf Tips

"Tips of leaves. a, acuminate or taper-pointed; b, acute; c, obtuse; d, truncate; e, retuse; f, emarginate…

"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 an isosceles triangle in an equilateral triangle.

Equilateral And Isosceles Triangles

An illustration showing an isosceles triangle in an equilateral triangle.

An illustration showing how to construct a center and radius of a circle that will tangent the three sides of a triangle. "Bisect two of the angles in the triangle, and the crossing C is the center of the required circle."

Construction Of The Center And Radius Of A Circle Tangent To Triangle Sides

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

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius of the circle and center C draw the arc DFE; with the same radius, and D and E as centers, set off the points A and B. Join A and B, B and C, C and A, which will be the required triangle."

Construction Of An Equilateral Triangle Inscribed In A Circle

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius…

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose base is equal to the sum of all the sides, and the height a equal to the appotem of the polygon. "The reason of this is that the area of two or more triangles ABC and ADC having a common or equal base b and equal height h are alike."

Area Of Regular Polygon Proof

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose…

An illustration showing how to construct an ellipse using a string. "Having given the two axes, set off from c half the great axis at a and b, which are the two focuses of the ellipse. Take an endless string as long as the three sides in the triangle abc, fix two pins or nails in the focuses, one in a and one in b, lay the string around a and b, stretch it with a pencil d, which then will describe the desired ellipse."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using a string. "Having given the two axes, set…

An illustration showing a triangle with sides b, c, and d inscribed in a circle with radius r.

Triangle Inscribed In A Circle

An illustration showing a triangle with sides b, c, and d inscribed in a circle with radius r.

An illustration showing a circle with radius r inscribed in a triangle with sides a, b, and c.

Circle Inscribed In A Triangle

An illustration showing a circle with radius r inscribed in a triangle with sides a, b, and c.

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

Exterior And Interior Angles Of A Triangle

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

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…

An illustration showing a circle with sectors D and E inscribed in a triangle with angles, A, B, and C.

Circle Inscribed In A Triangle

An illustration showing a circle with sectors D and E inscribed in a triangle with angles, A, B, and…

An illustration showing a model that illustrates the Pythagorean Theorem: a&sup2 + b&sup2 = c&sup2.

Model Of Pythagorean Theorem

An illustration showing a model that illustrates the Pythagorean Theorem: a² + b² = c².

An illustration of an acute triangle with the height/altitude labeled h.

Acute Triangle

An illustration of an acute triangle with the height/altitude labeled h.

An illustration of an obtuse triangle with the height/altitude labeled h.

Obtuse Triangle

An illustration of an obtuse triangle with the height/altitude labeled h.

An illustration of a right triangle inscribed in a semicircle.

Right Triangle Inscribed In A Semicircle

An illustration of a right triangle inscribed in a semicircle.

An illustration showing a model of a triangle that illustrates the following relationship: a:c = d:(b - d), d = (a × b) ÷ (c + a), v = v.

Model Of Geometric Proportions In A Triangle

An illustration showing a model of a triangle that illustrates the following relationship: a:c = d:(b…

An illustration showing a model of a circle with intersecting chords that illustrates the following relationship: a:c = b:d, ad = bc. Product of the means equals the product of the extremes.

Model Of Geometric Proportions In A Circle

An illustration showing a model of a circle with intersecting chords that illustrates the following…

Four types of angles: right, obtuse, acute, and straight.

Angles

Four types of angles: right, obtuse, acute, and straight.

"The triangle ABC is divided into 2 right triangles I and II. ABC is seen to be equal to 1/2 of the rectangle ABNO." -Foster, 1921

Area of Triangle

"The triangle ABC is divided into 2 right triangles I and II. ABC is seen to be equal to 1/2 of the…

"The child sees triangle ACB = triangle ADB, and that I + II = CA - DB; and so he sees that the area of triangle=1/2 area of rectangle whose base and altitude are the same as those of the triangles." -Foster, 1921

Area of Triangle

"The child sees triangle ACB = triangle ADB, and that I + II = CA - DB; and so he sees that the area…

"Fig. 3 shows triangle I = triangle II, III = IV, and so triangle ABC = 1/2 of rectangle ABDE. The fact is realized that the area of a triangle equals 1/2 the product of the base and altitude." -Foster, 1921

Area of Triangle

"Fig. 3 shows triangle I = triangle II, III = IV, and so triangle ABC = 1/2 of rectangle ABDE. The fact…

Illustration showing how to find the area of a hexagon using the triangles that make it up.

Area of Hexagon

Illustration showing how to find the area of a hexagon using the triangles that make it up.

"Diagram to illustrate the inferred structure in the vicinity of the "Triangle." Arkose conglomerate is represented by lines and ellipses, anterior basalt by the black areas, anterior shale by parallel lines, and main basalt by cross-hachure areas. The finer hachuring (and hence the deeper shade) corresponds to the higher blocks of the basalt." -Walcott, 1901

Basalt Diagram

"Diagram to illustrate the inferred structure in the vicinity of the "Triangle." Arkose conglomerate…

The region of the neck, from the side.

Side View of Neck

The region of the neck, from the side.

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…

This modern Tablet Architectural frame was in the style of the Italian Renaissance. It had the general shape of an erect triangle that has a cresting feature, free-ending upwards.

Tablet Frame

This modern Tablet Architectural frame was in the style of the Italian Renaissance. It had the general…

The pulpit Architectural frame was a German frame that was dated between 1595 to 1597. It had the general shape of an erect triangle that has a cresting feature, free-ending upwards.

Pulpit Frame

The pulpit Architectural frame was a German frame that was dated between 1595 to 1597. It had the general…

"The familiar cockles are among the most widely distributed of shells. The greatest number are furnished with regular ripples, generally obtuse, sometimes in ridges diverging from the point and armed with straight or curved spines, arranged in the oddest manner"

Cardium Aculeatum (Linnaeus)

"The familiar cockles are among the most widely distributed of shells. The greatest number are furnished…

Labeled shapes showing various measures of form.

Measures of Form

Labeled shapes showing various measures of form.

Showing different types of angles: right, acute, and obtuse.

Angles

Showing different types of angles: right, acute, and obtuse.

Showing different types of forms or shapes: rectangle, right triangle, acute triangle, and obtuse triangle.

Forms

Showing different types of forms or shapes: rectangle, right triangle, acute triangle, and obtuse triangle.

Showing different types of parallel prisms: rectangular, right triangular, acute triangular, and obtuse triangular.

Parallel Prisms

Showing different types of parallel prisms: rectangular, right triangular, acute triangular, and obtuse…

Showing different types of oblique prisms: rectangular, right triangular, acute triangular, and obtuse triangular.

Oblique Prisms

Showing different types of oblique prisms: rectangular, right triangular, acute triangular, and obtuse…

Four different types of forms or shapes: right triangle, isosceles triangle, rectangle, and circle.

Shapes

Four different types of forms or shapes: right triangle, isosceles triangle, rectangle, and circle.

Illustration showing that a circle may be considered as made up of triangles whose bases form the circumference.

Triangles Making Up A Circle

Illustration showing that a circle may be considered as made up of triangles whose bases form the circumference.

Illustration of a triangular prism; a prism whose bases are triangles.

Triangular Prism

Illustration of a triangular prism; a prism whose bases are triangles.

"The trunk appears to be composed of two parts, joined, and forming a more or less obtuse angle."

Trunk of the Meat-Fly

"The trunk appears to be composed of two parts, joined, and forming a more or less obtuse angle."

A cylindrical helix is a curve generated by a point moving uniformly around a cylinder and uniformly lengthwise of the cylinder at the some time. The hypotenuse of a right triangle will form one turn of a helix if it is wrapped around a cylinder. The base of the triangle is equal to the circumference of the cylinder and the altitude is the pitch of the helix.

Helix

A cylindrical helix is a curve generated by a point moving uniformly around a cylinder and uniformly…

An apparatus for verifying the parallelogram of forces. This method is used in physics for determining the force of vectors.

Gravesande's Apparatus

An apparatus for verifying the parallelogram of forces. This method is used in physics for determining…

"In the subfamily of the Zoanthidae, the polyps occur in clusters, and are multiplied by buds, rising from a common, creeping, root-like, fleshy base. This species possesses the power of considerably altering its shape; sometimes the mouth is depressed, and at others it is elevated into an obtuse cone."

Flabellum Pavonium (Lesson)

"In the subfamily of the Zoanthidae, the polyps occur in clusters, and are multiplied by buds, rising…

The triangles of the neck.

Triangles of the Neck

The triangles of the neck.

Angels sitting on either side of a box.

Triangular Doodad

Angels sitting on either side of a box.

Illustration showing intersecting straight lines meeting to form a triangle. It is formed by the intersection of the surface of a cone with a plane parallel to the axis and actually containing the axis.

Degenerate Conic Forming Triangle

Illustration showing intersecting straight lines meeting to form a triangle. It is formed by the intersection…

The suboccipital triangle.

Suboccipital Triangle

The suboccipital triangle.

The flag of Cuba was adopted on May 20, 1902, containing a field with five blue and white stripes, and a red triangle at the hoist with a white 5-pointed star. The flag was designed in 1848 for the liberation movement, which sought to detach Cuba from Spain. The flag was briefly hoisted in 1850 at Cardenas but was not officially adopted until 1902, when independence was granted by the US.

Cuban Flag

The flag of Cuba was adopted on May 20, 1902, containing a field with five blue and white stripes, and…

The main entrance through the circuit wall was made grand by the best known feature of Mycenae, the Lion Gate, through which passed a stepped ramp leading past circle A and up to the palace. The Lion Gate was built in the form of a 'Relieving Triangle' to support the weight of the stones. Two lionesses flank the central column that represents a god or goddess.

Lion Gate at Mycenæ

The main entrance through the circuit wall was made grand by the best known feature of Mycenae, the…

The Renaissance console is shaped in front-view like a pendant triangle. This console is found in a castle in Blois, France.

Renaissance Console

The Renaissance console is shaped in front-view like a pendant triangle. This console is found in a…

This modern French console has a front view like a pendant triangle.

Modern French Console

This modern French console has a front view like a pendant triangle.

The Or Ordinary in the dexter (right side) is a chief triangle sable (black).

Or Ordinary

The Or Ordinary in the dexter (right side) is a chief triangle sable (black).

The Argent Ordinary is in the sinister base a triangle gules (red).

Argent Ordinary

The Argent Ordinary is in the sinister base a triangle gules (red).

"In the apparatus shown... three forces act on a small body and are allowed to assume a position of equilibrium. A triangle is then constructed with sides parallel respectively to the three forces; it will be found by measurement that the sides are also the lengths proportional to the forces, and as will be seen the arrowheads point concurrently round the triangle.

Polygon of Forces

"In the apparatus shown... three forces act on a small body and are allowed to assume a position of…

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine the height of the tower, the hypotenuse, and distance of the tower from the object.

Triangle with Tower

An illustration of a triangle comprised of a tower and two lines. This illustration can be used to determine…

An illustration of a triangle comprised of a church and two lines. This illustration can be used to determine the height of the church steeple, the hypotenuse, and distance of the tower from object one and two.

Triangle with Church

An illustration of a triangle comprised of a church and two lines. This illustration can be used to…