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 9
... angle BAC equal to the angle EDF : the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC ...
... angle BAC equal to the angle EDF : the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC ...
Σελίδα 13
... angle BAC coincides with the angle EDF , and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c . Q.E.D. PROP . IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be ...
... angle BAC coincides with the angle EDF , and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c . Q.E.D. PROP . IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be ...
Σελίδα 14
... angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the 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 ...
... angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the 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 ...
Σελίδα 19
... angle CEA is equal to the remaining angle DEB . In the same manner it can be ... BAČ . F G Bisect ( I. 10. ) AC in E , join BE and produce it to F , and make ... angles ; therefore ( I. 4. ) 3. The base AB is equal to the base CF , and ...
... angle CEA is equal to the remaining angle DEB . In the same manner it can be ... BAČ . F G Bisect ( I. 10. ) AC in E , join BE and produce it to F , and make ... angles ; therefore ( I. 4. ) 3. The base AB is equal to the base CF , and ...
Σελίδα 20
... angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and opposite angle ABC ; to each of these ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q.E.D. PROP . XVIII . - ...
... angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and opposite angle ABC ; to each of these ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q.E.D. PROP . XVIII . - ...
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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