The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 83
... 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 ...
Side 84
... segment BAED be not greater than a semicircle , let BAD , BED be angles in it ; these also are equal to one another : draw AF to the centre , and produce it to C , and join CE : therefore the segment BADC is greater than a semicircle ...
... segment BAED be not greater than a semicircle , let BAD , BED be angles in it ; these also are equal to one another : draw AF to the centre , and produce it to C , and join CE : therefore the segment BADC is greater than a semicircle ...
Side 85
... segment ADB , and that si- milar segments of circles contain ( 11. def . 3. ) equal angles ; the angle ACB is equal ... segment AEB is equal to the seg- ment CFD . For , if the segment AEB be applied to the segment CFD , so as the point ...
... segment ADB , and that si- milar segments of circles contain ( 11. def . 3. ) equal angles ; the angle ACB is equal ... segment AEB is equal to the seg- ment CFD . For , if the segment AEB be applied to the segment CFD , so as the point ...
Side 86
... segment AEB , must ( 23. 3. ) coincide with the segment CFD , and therefore is equal to it . Wherefore similar segments , & c . Q. E. D. PROP . XXV . PROB . A SEGMENT of a circle being given to describe the circle of which it is the segment ...
... segment AEB , must ( 23. 3. ) coincide with the segment CFD , and therefore is equal to it . Wherefore similar segments , & c . Q. E. D. PROP . XXV . PROB . A SEGMENT of a circle being given to describe the circle of which it is the segment ...
Side 87
... segment ABC , which is therefore greater than a semicircle : wherefore a segment of a circle being given , the circle is de- scribed of which it is a segment . Which was to be done . PROP . XXVI . THEOR . In equal circles , equal angles ...
... segment ABC , which is therefore greater than a semicircle : wherefore a segment of a circle being given , the circle is de- scribed of which it is a segment . Which was to be done . PROP . XXVI . THEOR . In equal circles , equal angles ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore