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 σελίδες |
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Σελίδα 64
... touch a circle , when it meets the circle , and being produced does not cut it . O III . Circles are said to touch one another , which meet , but do not cut one another . IV . Straight lines are said to be equally distant from the ...
... touch a circle , when it meets the circle , and being produced does not cut it . O III . Circles are said to touch one another , which meet , but do not cut one another . IV . Straight lines are said to be equally distant from the ...
Σελίδα 69
... circle , & c . Q.E.D. PROP . V. - THEOREM . If two circles cut one another , they shall not have the same centre ... touch one another internally , they shall not have the same centre . Let the two circles ABC , CDE , touch one BOOK III ...
... circle , & c . Q.E.D. PROP . V. - THEOREM . If two circles cut one another , they shall not have the same centre ... touch one another internally , they shall not have the same centre . Let the two circles ABC , CDE , touch one BOOK III ...
Σελίδα 70
Euclid, Samuel A. GOOD. Let the two circles ABC , CDE , touch one another internally in the point C ; they have not ... circle ABC , ( I. Def . 15. ) 1. CF is equal to FB ; also , because F is the centre of the circle CDE , 2 . CF is ...
Euclid, Samuel A. GOOD. Let the two circles ABC , CDE , touch one another internally in the point C ; they have not ... circle ABC , ( I. Def . 15. ) 1. CF is equal to FB ; also , because F is the centre of the circle CDE , 2 . CF is ...
Σελίδα 74
... circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference of a circle cannot ... touch each other internally , the straight line which joins their centres , being produced , shall pass through the point ...
... circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference of a circle cannot ... touch each other internally , the straight line which joins their centres , being produced , shall pass through the point ...
Σελίδα 75
... circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point ; and let F be the centre of the circle ...
... circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point ; and let F be the centre of the circle ...
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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