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 86
... segments of circles upon the equal straight lines , AB , CD ; the segment AEB is equal to the segment CFD . E A B D For if the segment AEB be applied to the segment CFD , so that the point A may be on C , and the straight line AB on CD ...
... segments of circles upon the equal straight lines , AB , CD ; the segment AEB is equal to the segment CFD . E A B D For if the segment AEB be applied to the segment CFD , so that the point A may be on C , and the straight line AB on CD ...
Página 87
... segment . Let ABC be the given segment of a circle ; it is required to describe the circle of which it is the segment . Bisect ( I. 10. ) AC in D , and from the point D draw ( I. 11. ) DB , at right angles to AC ; and join AB . B A D ...
... segment . Let ABC be the given segment of a circle ; it is required to describe the circle of which it is the segment . Bisect ( I. 10. ) AC in D , and from the point D draw ( I. 11. ) DB , at right angles to AC ; and join AB . B A D ...
Página 88
... segment ABC , which is therefore greater than a semicircle . Wherefore a segment of a circle being given , the circle is described of which it is a segment . Which was to be done . PROP . XXVI . - THEOREM . In equal circles , equal ...
... segment ABC , which is therefore greater than a semicircle . Wherefore a segment of a circle being given , the circle is described of which it is a segment . Which was to be done . PROP . XXVI . - THEOREM . In equal circles , equal ...
Página 91
... segments ABC , ADC , and join BA , AD , DC : the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC , which is greater than a semicircle , is less than a right angle ; and the angle in the segment ADC ...
... segments ABC , ADC , and join BA , AD , DC : the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC , which is greater than a semicircle , is less than a right angle ; and the angle in the segment ADC ...
Página 92
... segment ABC falls without the right angle CAB , but the circumference of the less segment ADC falls within the right angle CAF . " And this is all that is meant , when in the Greek text , and the trans- lations from it , the angle of ...
... segment ABC falls without the right angle CAB , but the circumference of the less segment ADC falls within the right angle CAF . " And this is all that is meant , when in the Greek text , and the trans- lations from it , the angle of ...
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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