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 17
... base EG ; and be- cause DG is equal to DF , the angle DFG is equal ( 3.1 . ) to the angle DGF ; but the angle DGF is ... base of the one greater than the base of the other ; the an- gle contained by the sides of that which has the ...
... base EG ; and be- cause DG is equal to DF , the angle DFG is equal ( 3.1 . ) to the angle DGF ; but the angle DGF is ... base of the one greater than the base of the other ; the an- gle contained by the sides of that which has the ...
Página 25
... base AC is equal ( 1. 1. ) to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles ( 1. 1. ) each to each , to which the equal sides are opposite ; therefore the angle ACB is equal to the ...
... base AC is equal ( 1. 1. ) to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other angles ( 1. 1. ) each to each , to which the equal sides are opposite ; therefore the angle ACB is equal to the ...
Página 26
... base and between the same parallels , are equivalent to one another . ( SEE THE 2d and 3d figures . ) Let the parallelograms ABCD , EBCF be upon the same base BC , between the same parallels AF , BC ; the parallelogram ABCD is equal to ...
... base and between the same parallels , are equivalent to one another . ( SEE THE 2d and 3d figures . ) Let the parallelograms ABCD , EBCF be upon the same base BC , between the same parallels AF , BC ; the parallelogram ABCD is equal to ...
Página 27
... base EB is equal to the base FC , and the triangle EAB ( 1. 1. ) to the triangle FDC . Take the triangle FDC from the trapezium ABCF , and from the same trapezium take the triangle EAB ; the remainders will then be equal ( 3. Ax ...
... base EB is equal to the base FC , and the triangle EAB ( 1. 1. ) to the triangle FDC . Take the triangle FDC from the trapezium ABCF , and from the same trapezium take the triangle EAB ; the remainders will then be equal ( 3. Ax ...
Página 28
... base BC , and between the same pa- E A D F B rallels BC , EF ; but the triangle ABC is the half of the parallelogram ... base , and upon the same side of it , are between the same parallels . Let the equal triangles ABC , DBC be upon the ...
... base BC , and between the same pa- E A D F B rallels BC , EF ; but the triangle ABC is the half of the parallelogram ... base , and upon the same side of it , are between the same parallels . Let the equal triangles ABC , DBC be upon the ...
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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