Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 7
... equal ; an equian- gular polygon , one which has all its angles equal . 32. Two polygons are mutually equilateral , when they have their sides equal to each other , and placed in the same order ; that is to say , when follow- ing their ...
... equal ; an equian- gular polygon , one which has all its angles equal . 32. Two polygons are mutually equilateral , when they have their sides equal to each other , and placed in the same order ; that is to say , when follow- ing their ...
Página 9
... equal to two sides and the included angle in the other , the triangles will be identical , or equal in all respects ... angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF ...
... equal to two sides and the included angle in the other , the triangles will be identical , or equal in all respects ... angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF ...
Página 10
... angles at the base of an isosceles triangle are equal to one another : namely , those to which the equal sides are opposite . If the triangle ABC have the side AC equal to the side BC : then will the angle B be equal to the angle A. For ...
... angles at the base of an isosceles triangle are equal to one another : namely , those to which the equal sides are opposite . If the triangle ABC have the side AC equal to the side BC : then will the angle B be equal to the angle A. For ...
Página 11
... equal to AC , one of them is greater than the other : Let AB be the greater ... angles equal , each to each . Let the two triangles ABC , DEF , have their ... angle BGA , and the angle OF GEOMETRY . BOOK I. 11.
... equal to AC , one of them is greater than the other : Let AB be the greater ... angles equal , each to each . Let the two triangles ABC , DEF , have their ... angle BGA , and the angle OF GEOMETRY . BOOK I. 11.
Página 12
... equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the sum of the two angles BGA , CGA , ( Ax . 2. ) that is , the whole an- gle BAC equal to the whole angle BGC . Since , then , the two ...
... equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the sum of the two angles BGA , CGA , ( Ax . 2. ) that is , the whole an- gle BAC equal to the whole angle BGC . Since , then , the two ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore