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 6
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Página 34
... the base BC be terminated in the same point D , it is plain that ( I. 34. ) Each of the parallelograms ABCD , DBCF , is double 1 . of the triangle BDC ; and therefore ( Ax . 6. ) 2. The parallelograms 34 EUCLID'S ELEMENTS .
... the base BC be terminated in the same point D , it is plain that ( I. 34. ) Each of the parallelograms ABCD , DBCF , is double 1 . of the triangle BDC ; and therefore ( Ax . 6. ) 2. The parallelograms 34 EUCLID'S ELEMENTS .
Página 38
... parallelogram and a triangle be upon the same base , and between the same parallels , the parallelogram shall be double of the triangle . Let the parallelogram ABCD and the triangle EBC be upon 388 EUCLID'S ELEMENTS .
... parallelogram and a triangle be upon the same base , and between the same parallels , the parallelogram shall be double of the triangle . Let the parallelogram ABCD and the triangle EBC be upon 388 EUCLID'S ELEMENTS .
Página 39
... double of the triangle because the diameter AC divides it into two equal parts ; wherefore also 3. ABCD is double of the triangle EBC . Therefore , if a parallelogram , & c . Q.E.D. PROP . XLII . - PROBLEM . To describe a parallelogram ...
... double of the triangle because the diameter AC divides it into two equal parts ; wherefore also 3. ABCD is double of the triangle EBC . Therefore , if a parallelogram , & c . Q.E.D. PROP . XLII . - PROBLEM . To describe a parallelogram ...
Página 40
... double of the triangle AEC , because they are upon the same base EC , and between the same parallels EC , AG . Therefore ( Ax . 6. ) 4. The parallelogram FECG is equal to the triangle ABC , and it has one of its angles CEF equal ...
... double of the triangle AEC , because they are upon the same base EC , and between the same parallels EC , AG . Therefore ( Ax . 6. ) 4. The parallelogram FECG is equal to the triangle ABC , and it has one of its angles CEF equal ...
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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