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 3
... circumference cut off by the diameter . XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . " XX . Rectilineal figures are those which are contained by straight lines . XXI ...
... circumference cut off by the diameter . XIX . " A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . " XX . Rectilineal figures are those which are contained by straight lines . XXI ...
Σελίδα 65
... circumference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and the circumference . " VIII . An angle in a segment is the angle contained by two straight lines drawn . from any point in the ...
... circumference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and the circumference . " VIII . An angle in a segment is the angle contained by two straight lines drawn . from any point in the ...
Σελίδα 66
... line which bisects the other . PROP . II . THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B 66 EUCLID'S ELEMENTS .
... line which bisects the other . PROP . II . THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B 66 EUCLID'S ELEMENTS .
Σελίδα 67
... circumference ; the straight line drawn from A to B shall fall within the circle . C A E B For if AB do not fall within the circle , let it fall , if possible , without , as AEB ; find ( III . 1. ) D the centre of the circle ABC , and ...
... circumference ; the straight line drawn from A to B shall fall within the circle . C A E B For if AB do not fall within the circle , let it fall , if possible , without , as AEB ; find ( III . 1. ) D the centre of the circle ABC , and ...
Σελίδα 70
... circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and , of any others , that which is nearer to the line which passes through the centre is always greater than one more ...
... circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and , of any others , that which is nearer to the line which passes through the centre is always greater than one more ...
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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