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 50
... reason , also , 10 . HF is a square , and it is upon the side HG , which is equal ( I. 34. ) to AC ; therefore 11 . HF , CK , are the squares of AC , CB . And because the complement AG is equal ( I. 43. ) to the complement GE , and that ...
... reason , also , 10 . HF is a square , and it is upon the side HG , which is equal ( I. 34. ) to AC ; therefore 11 . HF , CK , are the squares of AC , CB . And because the complement AG is equal ( I. 43. ) to the complement GE , and that ...
Página 54
... reason , 2. PR is equal to RO ; and because CB is equal to BD , and GK to KN , ( I. 36. ) 3. The rectangle CK is equal to BN , and GR to RN ; but CK is equal ( I. 43. ) to RN , because they are the complements of the parallelogram CO ...
... reason , 2. PR is equal to RO ; and because CB is equal to BD , and GK to KN , ( I. 36. ) 3. The rectangle CK is equal to BN , and GR to RN ; but CK is equal ( I. 43. ) to RN , because they are the complements of the parallelogram CO ...
Página 56
... reason 4 . and therefore 5 . Each of the angles CEB , EBC , is half a right angle ; The whole AEB is a right angle . And because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( I. 29. ) to the interior ...
... reason 4 . and therefore 5 . Each of the angles CEB , EBC , is half a right angle ; The whole AEB is a right angle . And because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( I. 29. ) to the interior ...
Página 57
... ) 3 . Each of the angles CEA , EAC , is half a right angle . For the same reason , 4. Each of the angles CEB , EBC , is half a right angle ; therefore 5. The whole AEB is a right angle . 39 BOOK II . - PROP . IX . X. 57.
... ) 3 . Each of the angles CEA , EAC , is half a right angle . For the same reason , 4. Each of the angles CEB , EBC , is half a right angle ; therefore 5. The whole AEB is a right angle . 39 BOOK II . - PROP . IX . X. 57.
Página 71
... reason , 4. CF is greater than GF . Again , because GF , FE , are greater ( I. 20. ) than EG , and EG is equal to ED ; therefore take away 5 . the GF , FE , are greater than ED : common part FE , and ( Ax . 5. ) 6. The remainder GF is ...
... reason , 4. CF is greater than GF . Again , because GF , FE , are greater ( I. 20. ) than EG , and EG is equal to ED ; therefore take away 5 . the GF , FE , are greater than ED : common part FE , and ( Ax . 5. ) 6. The remainder GF is ...
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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