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 8
... shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 4. The straight line AL is equal to BC . Wherefore from the given point A a ...
... shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 4. The straight line AL is equal to BC . Wherefore from the given point A a ...
Página 21
... shown that it is not equal to AB ; therefore 3. AC is greater than AB . Wherefore the greater angle , & c . Q.E.D. PROP . XX . - THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
... shown that it is not equal to AB ; therefore 3. AC is greater than AB . Wherefore the greater angle , & c . Q.E.D. PROP . XX . - THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
Página 23
... shown that BA , AC , are greater than BE , EC ; much more then 5. BA , AC , are greater than BD , DC . Again , because the exterior angle of a triangle is greater than the inte- rior and opposite angle ( I. 16. ) 1 . than CED . The ...
... shown that BA , AC , are greater than BE , EC ; much more then 5. BA , AC , are greater than BD , DC . Again , because the exterior angle of a triangle is greater than the inte- rior and opposite angle ( I. 16. ) 1 . than CED . The ...
Página 26
... shown that it is not equal to it ; therefore 3. The angle BAC is greater than the angle EDF . Wherefore if two triangles , & c . Q.E.D. PROP . XXVI.- -THEOREM . If two triangles have two angles of the one equal to two angles of the ...
... shown that it is not equal to it ; therefore 3. The angle BAC is greater than the angle EDF . Wherefore if two triangles , & c . Q.E.D. PROP . XXVI.- -THEOREM . If two triangles have two angles of the one equal to two angles of the ...
Página 30
... shown that the angle AGK is equal to the angle 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 ...
... shown that the angle AGK is equal to the angle 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 ...
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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