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 43
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . D A B From the point A draw ( I. 11. ) AC at right angles to AB , and make ( I. 3. ) AD equal to AB , and through the ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . D A B From the point A draw ( I. 11. ) AC at right angles to AB , and make ( I. 3. ) AD equal to AB , and through the ...
Página 44
... squares described upon the sides which contain the right angle . Let ABC be a right - angled triangle having the right angle BAC ; the square described the side BC is equal to the upon described squares BA , AC . upon F B D E On BC ...
... squares described upon the sides which contain the right angle . Let ABC be a right - angled triangle having the right angle BAC ; the square described the side BC is equal to the upon described squares BA , AC . upon F B D E On BC ...
Página 45
... square GB is double of the triangle FBC , because these also are upon the same base FB , and between the same parallels FB , GC . But the doubles of equals are equal ( Ax . 6. ) to one ... square of AC ; BOOK I. - PROP . XLVII . XLVIII . 45.
... square GB is double of the triangle FBC , because these also are upon the same base FB , and between the same parallels FB , GC . But the doubles of equals are equal ( Ax . 6. ) to one ... square of AC ; BOOK I. - PROP . XLVII . XLVIII . 45.
Página 46
Euclid, Samuel A. GOOD. To each of these add the square of AC ; therefore 2 . The squares of DA , AC , are equal to the squares of BA , AC . But ( I. 47. ) 3. The square of DC is equal to the squares of DA , AC , because DAC is a right ...
Euclid, Samuel A. GOOD. To each of these add the square of AC ; therefore 2 . The squares of DA , AC , are equal to the squares of BA , AC . But ( I. 47. ) 3. The square of DC is equal to the squares of DA , AC , because DAC is a right ...
Página 48
... AC , shall be equal to the square of AB . A C B D F E Upon AB describe ( I. 46. ) the square ADEB ,, and through C draw N.B. To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC ...
... AC , shall be equal to the square of AB . A C B D F E Upon AB describe ( I. 46. ) the square ADEB ,, and through C draw N.B. To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC ...
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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