Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 páginas |
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Página 10
... multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and the angle ECD is the differ- ence between the two angles BCD , BCE . 10. When a straight line , meeting another straight line . makes the ...
... multiplied , or divided . Thus , the angle BCD is the sum of the two angles BCE , ECD ; and the angle ECD is the differ- ence between the two angles BCD , BCE . 10. When a straight line , meeting another straight line . makes the ...
Página 38
... Multiplying each of these equal quantities by B ( Axiom 1 ) . we obtain A : BXC D Multiplying each of these last equals by D , we have AXD = BXC . Cor . If there are three proportional quantities , the product of the two extremes is ...
... Multiplying each of these equal quantities by B ( Axiom 1 ) . we obtain A : BXC D Multiplying each of these last equals by D , we have AXD = BXC . Cor . If there are three proportional quantities , the product of the two extremes is ...
Página 42
... multiplying each of these equals by itself ( Axiom 1 ) , we have A'XD ' = B'XC2 ; and multiplying these last equals by A × D = B × C , we have A'X D ' B'XC ' . Therefore , by Prop . II . , - and A : B :: C : D ' , A ' : B ' :: C ' : D ...
... multiplying each of these equals by itself ( Axiom 1 ) , we have A'XD ' = B'XC2 ; and multiplying these last equals by A × D = B × C , we have A'X D ' B'XC ' . Therefore , by Prop . II . , - and A : B :: C : D ' , A ' : B ' :: C ' : D ...
Página 62
... to DEXKF . Hence the area of a trapezoid is equal to its altitude , multiplied by the line which joins the middle points of the sides which are not parallel . PROPOSITION VIII . THEOREM . If a straight line is 62 GEOMETRY .
... to DEXKF . Hence the area of a trapezoid is equal to its altitude , multiplied by the line which joins the middle points of the sides which are not parallel . PROPOSITION VIII . THEOREM . If a straight line is 62 GEOMETRY .
Página 75
... square on BC is to B the square on EF . A By similar triangles , we have ( Def . 3 ) AB : DE :: BC : EF . Also , BC : EF :: BC : EF . D CE F Multiplying together the corresponding terms of these pro portions , BOOK IV . 75.
... square on BC is to B the square on EF . A By similar triangles , we have ( Def . 3 ) AB : DE :: BC : EF . Also , BC : EF :: BC : EF . D CE F Multiplying together the corresponding terms of these pro portions , BOOK IV . 75.
Términos y frases comunes
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum given angle greater Hence Prop hyperbola inscribed intersection join latus rectum less Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side BC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC triangle DEF vertex vertices VIII
Pasajes populares
Página 17 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Página 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Página 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Página 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Página 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 32 - 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 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 30 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.