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 páginas |
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Página 15
... draw BE at right angles to AB ; and becanse ABC is a straight line , ( Def . 10. ) 1. The angle CBE is equal to the angle EBA ; in the same manner , because ABD is a straight line , 2. The angle DBE is equal to the angle EBA ; wherefore ...
... draw BE at right angles to AB ; and becanse ABC is a straight line , ( Def . 10. ) 1. The angle CBE is equal to the angle EBA ; in the same manner , because ABD is a straight line , 2. The angle DBE is equal to the angle EBA ; wherefore ...
Página 16
... draw a straight line perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance CD , describe ( Post . 3. ) the circle EGF meeting AB in F , G ; and bisect ( I. 10. ) FG in ...
... draw a straight line perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance CD , describe ( Post . 3. ) the circle EGF meeting AB in F , G ; and bisect ( I. 10. ) FG in ...
Página 17
... draw BE at right angles ( I. 11. ) to CD ; therefore ( Def . 10. ) 1. The angles CBE , EBD , are two right angles ; and because CBE is equal to the two angles CBA , ABE , together , add the angle EBD to each of these equals ; therefore ...
... draw BE at right angles ( I. 11. ) to CD ; therefore ( Def . 10. ) 1. The angles CBE , EBD , are two right angles ; and because CBE is equal to the two angles CBA , ABE , together , add the angle EBD to each of these equals ; therefore ...
Página 22
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD , be drawn from B , C , the ends of the side ...
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . Let the two straight lines BD , CD , be drawn from B , C , the ends of the side ...
Página 30
... GHF ; therefore also 3. AGK is equal to GKD ; and they are alternate angles ; therefore ( I. 27. ) 4. AB is parallel to CD . Wherefore straight lines , & c . Q.E.D. PROP . XXXI . - PROBLEM . To draw a 30 EUCLID'S ELEMENTS .
... GHF ; therefore also 3. AGK is equal to GKD ; and they are alternate angles ; therefore ( I. 27. ) 4. AB is parallel to CD . Wherefore straight lines , & c . Q.E.D. PROP . XXXI . - PROBLEM . To draw a 30 EUCLID'S ELEMENTS .
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Términos y frases comunes
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