New Elementary Geometry: With Practical Applications : a Shorter Course Upon the Basis of the Larger WorkRobert S. Davis & Company, 1874 - 176 páginas |
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Página 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 B C in the triangle АВС . A B D C E D C 177. The ...
... 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 B C in the triangle АВС . A B D C E D C 177. The ...
Página 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 D 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 D ABCD a parallelogram having the same base , A B , and ...
Página 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 ...
Página 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 . Let ABCD , A E G F be two rectangles ; then will ABCD be to ...
... 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 . Let ABCD , A E G F be two rectangles ; then will ABCD be to ...
Página 73
... altitude AD , are to each other as their bases , A B , A E. In like manner the two rectangles A E HD , AEG F ... altitude , provided we understand by this product the product of two numbers , one of which represents the number of linear ...
... altitude AD , are to each other as their bases , A B , A E. In like manner the two rectangles A E HD , AEG F ... altitude , provided we understand by this product the product of two numbers , one of which represents the number of linear ...
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New Elementary Geometry with Practical Applications Benjamin Greenleaf Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD ABCDEF alti altitude Theo angle A CD axis base multiplied bisect chord circum circumference circumscribed cone convex surface D E F diagonal diameter divided ELEMENTARY ALGEBRA ellipse entire surface equal Theo equivalent formed frustum greater GREENLEAF'S half the sum hence homologous homologous sides hypothenuse inches inscribed circle inscribed square intersection magnitudes mean proportional measured by half Metric System number of sides parallelogram parallelopipedon perimeter perpendicular prism PROBLEM quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo right pyramid rods Scholium SCHOOLS sector semicircle side A B side B C similar slant hight solid sphere is equal spherical square described square feet square root tangent THEOREM third triangles A B C triangular triangular prism tude vertex
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 61 - At a point in a given straight line to make an angle equal to a given angle.
Página 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Página 93 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 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.
Página 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...
Página 88 - FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.
Página 124 - But the solidity of each triangular prism is equal to the product of its base by its altitude ; and.