## New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |

### From inside the book

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**equivalent**which are not similar . Thus a circle may be**equivalent**to a square , and a triangle to a rec- tangle . 174. Equal Figures are such as , when applied the one to the other , coincide throughout ( 26 , Ax . 12 ) . Thus circles ... Page 69

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**equivalent**. Let A B CD , ABEF be two parallelograms having equal bases and equal altitudes ; then these par- allelograms are**equivalent**. D C F E A B Let the base of the one parallelo- gram be placed on that of the other , so that A B ... Page 70

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**equivalent**. 180. Cor . Any parallelogram is**equivalent**to a rectangle having the same base and altitude . THEOREM II . 181. If a triangle and a parallelogram have the same base and altitude , the triangle is**equivalent**to half the ... Page 71

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**equivalent**. THEOREM III . 184. Two rectangles having equal altitudes are to each other as their bases . Let ABCD , AEFD D F C be two rectangles having the common altitude AD ; they are to each other as their bases A B , A E. A E B ... Page 73

... to A A B , and produce CD to F. B Then the parallelogram A B C D is

... to A A B , and produce CD to F. B Then the parallelogram A B C D is

**equivalent**to the rectangle A B E F , which has the same base , A B , and the same altitude , BE ( Theo . I. Cor . ) . But the rectangle AB E F 7 BOOK IV . 73.### Other editions - View all

### Common terms and phrases

A B C D ABCD ABCDEF alti altitude altitude Theo angle A CD axis base multiplied bisect chord circumference circumscribed cone convex surface diagonal diameter divided Elementary Algebra ellipse entire surface equal Theo equivalent frustum greater GREENLEAF'S NEW MATHEMATICAL Greenleaf's New Series half the sum hence homologous homologous sides hypothenuse inches inscribed circle magnitudes MATHEMATICAL SERIES mean proportional measured by half number of sides parallelogram parallelopipedon Parker's Exercises perimeter perpendicular prism PROBLEM radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo rods Scholium School secant line side A B side B C similar slant hight solid sphere is equal spherical square described square feet THEOREM triangles A B C triangular triangular prism vertex zoid

### Popular passages

Page 23 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.

Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 61 - At a point in a given straight line to make an angle equal to a given angle.

Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.

Page 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.

Page 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...

Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...

Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.