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
Euclid, Samuel A. GOOD. PROPOSITION I. - PROBLEM . To describe an equilateral triangle upon a 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 ...
Euclid, Samuel A. GOOD. PROPOSITION I. - PROBLEM . To describe an equilateral triangle upon a 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 ...
Σελίδα 8
... straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut ...
... straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut ...
Σελίδα 13
... straight line BC upon EF ; 1 . The point C shall coincide with the point F , because BC is equal to EF ; therefore ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it ...
... straight line BC upon EF ; 1 . The point C shall coincide with the point F , because BC is equal to EF ; therefore ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it ...
Σελίδα 14
... straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts ...
... straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts ...
Σελίδα 15
... straight line makes with another straight line are equal to one another , each of them is called ( Def . 10. ) a right angle ; therefore , 4. Each of the angles DCF , ECF , is a right angle . Wherefore , from the given point C , in the ...
... straight line makes with another straight line are equal to one another , each of them is called ( Def . 10. ) a right angle ; therefore , 4. Each of the angles DCF , ECF , is a right angle . Wherefore , from the given point C , in the ...
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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 THEOREM touches the circle triangle ABC twice the rectangle