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 σελίδες |
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Σελίδα 17
... segment ; that is , they cannot " coincide in part , without coinciding altogether . " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the inter- sections of one ...
... segment ; that is , they cannot " coincide in part , without coinciding altogether . " IV . A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the inter- sections of one ...
Σελίδα 66
... segment of a circle is the figure con- tained by a straight line , and the arch which it cuts off . 1 VI . An angle in a segment is the angle ELEMENTS.
... segment of a circle is the figure con- tained by a straight line , and the arch which it cuts off . 1 VI . An angle in a segment is the angle ELEMENTS.
Σελίδα 67
... segment . VII . And an angle is said to insist or stand upon the arch intercepted between the straight lines which ... segments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP . 1. PROB . To ...
... segment . VII . And an angle is said to insist or stand upon the arch intercepted between the straight lines which ... segments of a circle , are those in which the an- gles are equal , or which contain equal angles . PROP . 1. PROB . To ...
Σελίδα 80
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED : The angles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And . first , let the segment ...
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED : The angles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And . first , let the segment ...
Σελίδα 81
... segment BAED be not greater than a semicircle , let BAD , BED be an- gles in it ; these also are equal to one ano- ther . Draw AF to the centre , and produce B to C , and join CE : Therefore the seg- ment BADC is greater than a ...
... segment BAED be not greater than a semicircle , let BAD , BED be an- gles in it ; these also are equal to one ano- ther . Draw AF to the centre , and produce B to C , and join CE : Therefore the seg- ment BADC is greater than a ...
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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