The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 71
... circumference ; and BF is greater than CF , and CF than GF . Also there can be drawn only two equal straight lines from the point F to the circumference , one upon each side of the shortest line FD . At the point E , in the straight ...
... circumference ; and BF is greater than CF , and CF than GF . Also there can be drawn only two equal straight lines from the point F to the circumference , one upon each side of the shortest line FD . At the point E , in the straight ...
Σελίδα 72
... circumference , whereof DA passes through the centre . Of those which fall upon the concave part of the circumference AEFC , the greatest is AD which passes through the centre ; and the nearer to it is always greater than the more ...
... circumference , whereof DA passes through the centre . Of those which fall upon the concave part of the circumference AEFC , the greatest is AD which passes through the centre ; and the nearer to it is always greater than the more ...
Σελίδα 73
... circumference , one upon each side of the least . At the point M , in the straight line MD , make ( I. 23. ) the angle DMB equal to the angle DMK , and join DB . And because MK is equal to MB , and MD common to the triangle KMD , BMD ...
... circumference , one upon each side of the least . At the point M , in the straight line MD , make ( I. 23. ) the angle DMB equal to the angle DMK , and join DB . And because MK is equal to MB , and MD common to the triangle KMD , BMD ...
Σελίδα 74
... circumference FAB cut the circumference DEF in more than two points , viz . in B , G , F. A B Ꭰ H E K C Take the centre K ( III . 3. ) of the circle ABC , and join KB , KG , KF . And because within the circle DEF there is taken the ...
... circumference FAB cut the circumference DEF in more than two points , viz . in B , G , F. A B Ꭰ H E K C Take the centre K ( III . 3. ) of the circle ABC , and join KB , KG , KF . And because within the circle DEF there is taken the ...
Σελίδα 76
... circumference of each of the circles , ( III . 2. ) 1. The straight line BD falls within each of the circles EBF , ABC ; and their centres are ( III . 1. Cor . ) in the straight line GH which bisects BD at right angles : therefore ( III ...
... circumference of each of the circles , ( III . 2. ) 1. The straight line BD falls within each of the circles EBF , ABC ; and their centres are ( III . 1. Cor . ) in the straight line GH which bisects BD at right angles : therefore ( III ...
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AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle