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 5
... produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight ...
... produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight ...
Página 6
... these straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . " PROPOSITION I. - PROBLEM . To describe an equilateral triangle 6 EUCLID'S ELEMENTS .
... these straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . " PROPOSITION I. - PROBLEM . To describe an equilateral triangle 6 EUCLID'S ELEMENTS .
Página 7
... produce ( Post . 2. ) the straight lines DA , DB to E and F. From the centre B at the distance BC , describe ( Post . 3. ) the circle CGH , and from the centre D , at the distance DG , describe the circle GKL . AL shall be equal to BC ...
... produce ( Post . 2. ) the straight lines DA , DB to E and F. From the centre B at the distance BC , describe ( Post . 3. ) the circle CGH , and from the centre D , at the distance DG , describe the circle GKL . AL shall be equal to BC ...
Página 10
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC , be produced to D and E , the angle ABC shall be equal ...
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC , be produced to D and E , the angle ABC shall be equal ...
Página 12
... produce AC , AD to E , F ; therefore because AC is equal to AD in the triangle ACD , ( I. 5. ) the angles upon the other side of the base CD , namely , 1. The angles ECD , FDC , are equal to one another ; but the angle ECD is greater ...
... produce AC , AD to E , F ; therefore because AC is equal to AD in the triangle ACD , ( I. 5. ) the angles upon the other side of the base CD , namely , 1. The angles ECD , FDC , are equal to one another ; but the angle ECD is greater ...
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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