Elements of Geometry and Conic SectionsHarper, 1849 - 226 sider |
Inni boken
Resultat 1-5 av 23
Side 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 , BCĚ . 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 , BCĚ . 10. When a straight line , meeting another straight line , makes the ...
Side 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 equal ...
... 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 equal ...
Side 42
... multiplying each of these equals by itself ( Axiom 1 ) , we have A'x D'B ' XC2 ; = and multiplying these last equals by AxD - B × C , we have A3 × D'B ' × C3 . Therefore , by Prop . II . , and A ' : B ' :: C ' : D ' , A ' : B ' :: C ...
... multiplying each of these equals by itself ( Axiom 1 ) , we have A'x D'B ' XC2 ; = and multiplying these last equals by AxD - B × C , we have A3 × D'B ' × C3 . Therefore , by Prop . II . , and A ' : B ' :: C ' : D ' , A ' : B ' :: C ...
Side 62
... DEX KF . 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 .
... DEX KF . 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 .
Side 75
... as the square on BC is to B the square on EF . A D By similar triangles , we have ( Def . 3 ) Also , AB : DE :: BC : EF . BC : EF :: BC : EF . CE Multiplying together the corresponding terms of these pro- portions , BOOK IV . 75.
... as the square on BC is to B the square on EF . A D By similar triangles , we have ( Def . 3 ) Also , AB : DE :: BC : EF . BC : EF :: BC : EF . CE Multiplying together the corresponding terms of these pro- portions , BOOK IV . 75.
Andre utgaver - Vis alle
ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained 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 greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin 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 Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Populære avsnitt
Side 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Side 27 - VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the...
Side 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Side 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.
Side 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.
Side 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.
Side 15 - 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.
Side 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.
Side 148 - I.), that every section of a sphere made by a plane is a circle.