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 34
... ABCD , EBCF , be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD shall be equal to the parallelogram EBCF . B B AED F B C If the sides AD , DF , of the parallelograms ABCD , DBCF , opposite to the ...
... ABCD , EBCF , be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD shall be equal to the parallelogram EBCF . B B AED F B C If the sides AD , DF , of the parallelograms ABCD , DBCF , opposite to the ...
Página 35
... ABCD , DBCF , are equal to one another . But if the sides 4D , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( I. 34. ) to BC ...
... ABCD , DBCF , are equal to one another . But if the sides 4D , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( I. 34. ) to BC ...
Página 36
... ABCD , because they are upon the same base BC , and between the same parallels BC , AH . For the like reason 5. The parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore ...
... ABCD , because they are upon the same base BC , and between the same parallels BC , AH . For the like reason 5. The parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore ...
Página 38
... a 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 .
... a 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
... ABCD is 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 ...
... ABCD is 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 ...
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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