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 7
... given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from the centre B ...
... given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from the centre B ...
Σελίδα 8
... circle CGH , ( Def . 15. ) 1. BC is equal to BG ; and because D is the centre of the circle GLK , 2. DL is equal to ... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done ...
... circle CGH , ( Def . 15. ) 1. BC is equal to BG ; and because D is the centre of the circle GLK , 2. DL is equal to ... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done ...
Σελίδα 16
... circle EGF meeting AB in F , G ; and bisect ( I. 10. ) FG in H , and join CH ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . C E II G B D Join CF , CG ; and because FH is equal to ...
... circle EGF meeting AB in F , G ; and bisect ( I. 10. ) FG in H , and join CH ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . C E II G B D Join CF , CG ; and because FH is equal to ...
Σελίδα 23
... given straight lines , but any two whatever of these must be greater than the third , ( I. 20. ) Let A , B , C , be ... circle DKL ; and from the centre G , at the distance GH , describe another circle HLK ; and join KF , KG ; the ...
... given straight lines , but any two whatever of these must be greater than the third , ( I. 20. ) Let A , B , C , be ... circle DKL ; and from the centre G , at the distance GH , describe another circle HLK ; and join KF , KG ; the ...
Σελίδα 24
... circle LKH , 3. GH is equal to GK ; but GH is equal to C ; therefore also 4. GK is equal to C ; and FG is equal ... given straight lines A , B , C. Which was to be done . PROP . XXIII . — PROBLEM . At a given point in a given ...
... circle LKH , 3. GH is equal to GK ; but GH is equal to C ; therefore also 4. GK is equal to C ; and FG is equal ... given straight lines A , B , C. Which was to be done . PROP . XXIII . — PROBLEM . At a given point in a given ...
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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