Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 sider |
Inni boken
Resultat 1-5 av 21
Side 36
... measuring unit is contained A B 15 times in A and 24 times in B , then the ratio of A to B is that of 15 to 24. And although it may be difficult to find this measuring unit , we may still conceive it to exist ; or , if there is no unit ...
... measuring unit is contained A B 15 times in A and 24 times in B , then the ratio of A to B is that of 15 to 24. And although it may be difficult to find this measuring unit , we may still conceive it to exist ; or , if there is no unit ...
Side 55
... measured by the arc BE ; hence the angle BAE is measured by the half of BE . For the same reason , the angle DAE is measured by half the arc DE . Therefore , the whole angle BAD is meas- ured by half the arc BD . Second . Let C , the ...
... measured by the arc BE ; hence the angle BAE is measured by the half of BE . For the same reason , the angle DAE is measured by half the arc DE . Therefore , the whole angle BAD is meas- ured by half the arc BD . Second . Let C , the ...
Side 56
... measured by half an arc less than semicircumference . Every angle inscribed in a segment less than a semicircle is an obtuse an- B gle , for it is measured by half an arc greater than a semicircumference . E D Cor . 4. The opposite ...
... measured by half an arc less than semicircumference . Every angle inscribed in a segment less than a semicircle is an obtuse an- B gle , for it is measured by half an arc greater than a semicircumference . E D Cor . 4. The opposite ...
Side 61
... measured by the product of AB by AF . For , upon the base AB , construct a rectangle having the altitude AF ; the par- allelogram ABCD is equivalent to the rec- tangle ABEF ( Prop . I. , Cor . ) . But the rectangle ABEF is measured by ...
... measured by the product of AB by AF . For , upon the base AB , construct a rectangle having the altitude AF ; the par- allelogram ABCD is equivalent to the rec- tangle ABEF ( Prop . I. , Cor . ) . But the rectangle ABEF is measured by ...
Side 62
... measured by half the product of DE , by the sum of its sides AB , CD . Bisect BC in F , and through F draw GH parallel to AD , and produce DC to A H. In the two triangles BFG , CFH , the side BF is equal to CF by construction , the ...
... measured by half the product of DE , by the sum of its sides AB , CD . Bisect BC in F , and through F draw GH parallel to AD , and produce DC to A H. In the two triangles BFG , CFH , the side BF is equal to CF by construction , the ...
Vanlige uttrykk og setninger
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
Populære avsnitt
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 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
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 101 - When you have proved that the three angles of every triangle are equal to two right angles...
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 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Side 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.
Side 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.
Side 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.