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

### From inside the book

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**hypothenuse**and a side of the one equal to the**hypothenuse**and a side of the other , each to each , the triangles are equal . Let the two right - angled A triangles ABC , BOOK I. 23. Page 24

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**hypothenuse**A C equal to D F , and the side AB equal to DE ; then will the triangle A B C be equal to the triangle DEF . B G D CE F. The two triangles are evidently equal , if the sides B C and EF are equal ( Theo . XIII . ) . If it be ... Page 76

... described on the half A B. 194. Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) 2 = a2 + 2ab + b2 . E H D I A B C THEOREM IX . 195. The square described on the

... described on the half A B. 194. Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) 2 = a2 + 2ab + b2 . E H D I A B C THEOREM IX . 195. The square described on the

**hypothenuse**76 ELEMENTARY GEOMETRY . Page 77

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**hypothenuse**BC will be equivalent to the sum of the H squares on the sides BA , A C. On B C describe the square BCGF ...**hypothenuses**BN , BC are equal ( Theo . V. Cor . , Bk . I. ) . But BC is equal to BF ; therefore BN is equal to B F ... Page 78

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**hypothenuse**diminished by the square of the other side ; thus , A B2 is equivalent to B C2 — A C2 . 197. Cor . 2. The square described on D the diagonal of a square is equivalent to double the square described on a side . For let ABCD ...### 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.