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 23
... reason , 2 . The exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than CEB ; much more then 3. The angle BDC is greater than the angle BAC . Therefore , if from the ...
... reason , 2 . The exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is greater than CEB ; much more then 3. The angle BDC is greater than the angle BAC . Therefore , if from the ...
Página 35
... reason , EF is equal to BC ; wherefore ( Ax . 1. ) 1. AD is equal to EF ; and DE is common ; therefore ( Ax . 2. or 3. ) 2. The whole , or the remainder , AE is equal to the whole , or the remainder , DF ; AB also is equal ( I. 34. ) to ...
... reason , EF is equal to BC ; wherefore ( Ax . 1. ) 1. AD is equal to EF ; and DE is common ; therefore ( Ax . 2. or 3. ) 2. The whole , or the remainder , AE is equal to the whole , or the remainder , DF ; AB also is equal ( I. 34. ) to ...
Página 36
... reason 5. The parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q.E.D. PROP . XXXVII . - THEOREM . Triangles upon the same base and between the ...
... reason 5. The parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q.E.D. PROP . XXXVII . - THEOREM . Triangles upon the same base and between the ...
Página 40
... reason , 3. The triangle KGC is equal to the triangle KFC . Then because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; ( Ax . 2. ) 4. The triangle AEK together with the triangle KGC is equal to the ...
... reason , 3. The triangle KGC is equal to the triangle KFC . Then because the triangle AEK is equal to the triangle AHK , and the triangle KGC to KFC ; ( Ax . 2. ) 4. The triangle AEK together with the triangle KGC is equal to the ...
Página 44
... reason 2. AB and AH are in the same straight line . And because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and ( Ax . 2. ) 3. The whole angle DBA is equal to the whole FBC ...
... reason 2. AB and AH are in the same straight line . And because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and ( Ax . 2. ) 3. The whole angle DBA is equal to the whole FBC ...
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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