New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 69
... Altitude of a Triangle is the perpendicular , which measures the distance of any one of its vertices from the opposite side taken as a base ; as the perpendicular A D let fall on the base BC in the triangle А В С. A B DC 177. The Altitude ...
... Altitude of a Triangle is the perpendicular , which measures the distance of any one of its vertices from the opposite side taken as a base ; as the perpendicular A D let fall on the base BC in the triangle А В С. A B DC 177. The Altitude ...
Page 70
... altitude . THEOREM II . 181. If a triangle and a parallelogram have the same base and altitude , the triangle is equivalent to half the parallelogram . Let ABE be a triangle , and ABCD a parallelogram having the same base , A B , and ...
... altitude . THEOREM II . 181. If a triangle and a parallelogram have the same base and altitude , the triangle is equivalent to half the parallelogram . Let ABE be a triangle , and ABCD a parallelogram having the same base , A B , and ...
Page 71
... altitude , or having the same altitude and half of the same base . 183. Cor . 2. All triangles which have equal bases and altitudes are equivalent . THEOREM III . 184. Two rectangles having equal altitudes are to each other as their ...
... altitude , or having the same altitude and half of the same base . 183. Cor . 2. All triangles which have equal bases and altitudes are equivalent . THEOREM III . 184. Two rectangles having equal altitudes are to each other as their ...
Page 72
... altitudes , are to each other as their bases A B , A E. THEOREM IV . 185. Any two rectangles are to each other as the prod- ucts of their bases multiplied by their altitudes . H D C Let ABCD , A EGF be two rectangles ; then will ABCD be ...
... altitudes , are to each other as their bases A B , A E. THEOREM IV . 185. Any two rectangles are to each other as the prod- ucts of their bases multiplied by their altitudes . H D C Let ABCD , A EGF be two rectangles ; then will ABCD be ...
Page 73
... altitude A D , are to each other as their bases , A B , A E. In like manner the two rectangles A E HD , AEGF ... altitude , provided we understand by this product the product of two numbers , one of which represents the number of ...
... altitude A D , are to each other as their bases , A B , A E. In like manner the two rectangles A E HD , AEGF ... altitude , provided we understand by this product the product of two numbers , one of which represents the number of ...
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Common terms and phrases
A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
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.