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 ... remaining angles of the other , and be equal to them , viz . 6. The angle ABC shall be equal to the angle DEF ...
... angle BAC equal to the angle EDF : the base BC shall be equal to the base EF ; and the triangle ABC to the triangle ... remaining angles of the other , and be equal to them , viz . 6. The angle ABC shall be equal to the angle DEF ...
Σελίδα 10
... angle FAG common to the two triangles AFC , AGB ; therefore ( I. 4. ) 1. The base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other ...
... angle FAG common to the two triangles AFC , AGB ; therefore ( I. 4. ) 1. The base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other ...
Σελίδα 18
... angles ( Hyp . ) ; therefore ( Ax . 1. ) 2. The angles CBA , ABE , are equal to the angles CBA , ABD . Take away the common angle ABC , and ( Ax . 3. ) 3 . The remaining angle ABE is equal to the remaining angle ABD , the less to the ...
... angles ( Hyp . ) ; therefore ( Ax . 1. ) 2. The angles CBA , ABE , are equal to the angles CBA , ABD . Take away the common angle ABC , and ( Ax . 3. ) 3 . The remaining angle ABE is equal to the remaining angle ABD , the less to the ...
Σελίδα 19
... remaining angle CEA is equal to the remaining angle DEB . In the same manner it can be demonstrated that 5. The angles CEB , 4ED , are equal . Therefore , if two straight lines , & c . Q.E.D. COR . 1. - From this it is manifest ...
... remaining angle CEA is equal to the remaining angle DEB . In the same manner it can be demonstrated that 5. The angles CEB , 4ED , are equal . Therefore , if two straight lines , & c . Q.E.D. COR . 1. - From this it is manifest ...
Σελίδα 29
... angles , and that AGH , BGH , are also equal ( I. 13. ) to two right angles , 1. The angles AGH , BGH , are equal to the angles BGH , GHD . Take away the common angle BGH ; therefore 2. The remaining angle AGH is equal to the remaining ...
... angles , and that AGH , BGH , are also equal ( I. 13. ) to two right angles , 1. The angles AGH , BGH , are equal to the angles BGH , GHD . Take away the common angle BGH ; therefore 2. The remaining angle AGH is equal to the remaining ...
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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