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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 47
... diameter AC divides it into two equal parts ; where- fore ABCD is also double of the trian- gle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB . B D E To describe a parallelogram that shall be equal to a given ...
... diameter AC divides it into two equal parts ; where- fore ABCD is also double of the trian- gle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB . B D E To describe a parallelogram that shall be equal to a given ...
Página 48
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other ...
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other ...
Página 56
... diameter of a square are likewise squares . PROP . V. THEOR . If a straight line be divided into two equal parts , and also into two un- equal parts ; the rectangle contained by the unequal parts , together with square of the line ...
... diameter of a square are likewise squares . PROP . V. THEOR . If a straight line be divided into two equal parts , and also into two un- equal parts ; the rectangle contained by the unequal parts , together with square of the line ...
Página 64
... diameters of any parallelogram is equal to the sum of the squares of the sides of the parallelogram . Let ABCD be a parallelogram , of which the diameters are AC and BD ; the sum of the squares of AC and BD is equal to the sum of the ...
... diameters of any parallelogram is equal to the sum of the squares of the sides of the parallelogram . Let ABCD be a parallelogram , of which the diameters are AC and BD ; the sum of the squares of AC and BD is equal to the sum of the ...
Página 65
... . From this demonstration , it is manifest that the diameters of every parallelogram bisect one another . T OF GEOMETRY . BOOK III . DEFINITIONS . A. T OF GEOMETRY . BOOK II . 65 COR. From this demonstration, it is manifest that ...
... . From this demonstration , it is manifest that the diameters of every parallelogram bisect one another . T OF GEOMETRY . BOOK III . DEFINITIONS . A. T OF GEOMETRY . BOOK II . 65 COR. From this demonstration, it is manifest that ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore