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 40
... passes , and BK , KD , the other parallelograms which make up the whole figure ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . A H K 1 . B G Because ABCD is a parallelogram , and AC ...
... passes , and BK , KD , the other parallelograms which make up the whole figure ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . A H K 1 . B G Because ABCD is a parallelogram , and AC ...
Σελίδα 67
... pass through the centre , it shall cut it at right angles ; and conversely , if it cut it at right angles , it shall bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre , bisect any straight line AB ...
... pass through the centre , it shall cut it at right angles ; and conversely , if it cut it at right angles , it shall bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre , bisect any straight line AB ...
Σελίδα 68
... pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD , two straight lines in it which cut one another in the point E , and do not both pass through the centre ; AC , BD , do not bisect one another ...
... pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD , two straight lines in it which cut one another in the point E , and do not both pass through the centre ; AC , BD , do not bisect one another ...
Σελίδα 69
... pass through the centre , it shall cut it at right angles ( III . 3. ) ; wherefore · 2. FEB is a right angle : and FEA was shown to be a right angle ; therefore 3. FEA is equal to the angle FEB , the less to the greater , which is ...
... pass through the centre , it shall cut it at right angles ( III . 3. ) ; wherefore · 2. FEB is a right angle : and FEA was shown to be a right angle ; therefore 3. FEA is equal to the angle FEB , the less to the greater , which is ...
Σελίδα 70
... passes through the centre is always greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a circle , and ...
... passes through the centre is always greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a circle , and ...
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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