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 62
... distance GB , or GF , describe the semicircle BHF , and produce DE to H : the square described upon EH shall be equal to the given rectilineal figure 4 . H B G E Join GH ; and because the straight line BF is 62 EUCLID'S ELEMENTS . to ...
... distance GB , or GF , describe the semicircle BHF , and produce DE to H : the square described upon EH shall be equal to the given rectilineal figure 4 . H B G E Join GH ; and because the straight line BF is 62 EUCLID'S ELEMENTS . to ...
Σελίδα 81
... distance AE , describe the circle AFG ; from the point D draw ( I. 11. ) FD at right angles to AE ; and join EBF , AB : AB touches the circle BCD . A D CE F B Because E is the centre of the circles BCD , AFG ; ( I. Def . 15. ) 1. EA is ...
... distance AE , describe the circle AFG ; from the point D draw ( I. 11. ) FD at right angles to AE ; and join EBF , AB : AB touches the circle BCD . A D CE F B Because E is the centre of the circles BCD , AFG ; ( I. Def . 15. ) 1. EA is ...
Σελίδα 87
... distance of any of the three DA , DB , DC , describe a circle ; this shall pass through the other points ; and the circle of which ABC is a segment is described : and because the centre D is in AC , 3. The segment ABC is a semicircle ...
... distance of any of the three DA , DB , DC , describe a circle ; this shall pass through the other points ; and the circle of which ABC is a segment is described : and because the centre D is in AC , 3. The segment ABC is a semicircle ...
Σελίδα 88
Euclid, Samuel A. GOOD. From the centre E , at the distance of any of the three AE , EB , EC , describe a circle ; this shall pass through the other points ; and the circle of which ABC is a segment is described . And it is evident ...
Euclid, Samuel A. GOOD. From the centre E , at the distance of any of the three AE , EB , EC , describe a circle ; this shall pass through the other points ; and the circle of which ABC is a segment is described . And it is evident ...
Σελίδα 94
... distance FB , describe the semicircle AHB ; therefore ( III . 31. ) at C. The angle AHB in the semicircle is equal to the right angle But if the angle C be not a right angle : II E G F H F B G E D At the point in the straight line AB ...
... distance FB , describe the semicircle AHB ; therefore ( III . 31. ) at C. The angle AHB in the semicircle is equal to the right angle But if the angle C be not a right angle : II E G F H F B G E D At the point in the straight line AB ...
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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