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 8
... doubles of the same thing , are equal to one another . 7. Things which are halves of the same thing , are equal to one another . 8. Two magnitudes , lines , surfaces , or solids , are equal , if , when applied to each other , they ...
... doubles of the same thing , are equal to one another . 7. Things which are halves of the same thing , are equal to one another . 8. Two magnitudes , lines , surfaces , or solids , are equal , if , when applied to each other , they ...
Página 26
... double ( 28. 1. ) of the triangle BDC ; and they are therefore equal to one another . € A B D and F But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then ...
... double ( 28. 1. ) of the triangle BDC ; and they are therefore equal to one another . € A B D and F But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then ...
Página 29
... double of the triangle . Let the parallelogram ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is ...
... double of the triangle . Let the parallelogram ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is ...
Página 31
... double of the triangle BFC because these also are upon the same base FB , and between the same parallels FB , GC . Now the doubles of equals are equal ( 6. Ax . ) to one another ; therefore the parallelogram BL is equal to the square GB ...
... double of the triangle BFC because these also are upon the same base FB , and between the same parallels FB , GC . Now the doubles of equals are equal ( 6. Ax . ) to one another ; therefore the parallelogram BL is equal to the square GB ...
Página 39
... double of the triangle AEC . And the parallel- ogram FECG is likewise double ( 35. 1. ) of the triangle AEC , be- D B E C cause it is upon the same base , and between the same parallels : There- fore the parallelogram FECG is equal to ...
... double of the triangle AEC . And the parallel- ogram FECG is likewise double ( 35. 1. ) of the triangle AEC , be- D B E C cause it is upon the same base , and between the same parallels : There- fore the parallelogram FECG is equal to ...
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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