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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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 9
... angles to which the equal sides are opposite shall be equal , each to each . Which was to be demonstrated . PROP . V.THEOREM . The angles at the base of 18 BOOK I. - PROP . IV . 9 shall be equal, each to each, viz. ...
... angles to which the equal sides are opposite shall be equal , each to each . Which was to be demonstrated . PROP . V.THEOREM . The angles at the base of 18 BOOK I. - PROP . IV . 9 shall be equal, each to each, viz. ...
Σελίδα 10
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF , are also equal ; therefore 6. The remaining angle ABC is equal to the remaining angle ACB , which are the angles at the base ...
... demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF , are also equal ; therefore 6. The remaining angle ABC is equal to the remaining angle ACB , which are the angles at the base ...
Σελίδα 12
... demonstrated to be greater than it , which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore because AC is equal to AD in the triangle ACD , ( I. 5. ) the angles ...
... demonstrated to be greater than it , which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore because AC is equal to AD in the triangle ACD , ( I. 5. ) the angles ...
Σελίδα 15
... demonstrated that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD , have the seg- ment AB common to both of them . E A B Ꭰ C From the point B draw BE at right angles to AB ...
... demonstrated that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD , have the seg- ment AB common to both of them . E A B Ꭰ C From the point B draw BE at right angles to AB ...
Σελίδα 17
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( Ax . 1. ) to one another ; therefore 4. The angles CBE , EBD , are equal to the angles DBA , ABC ; but CBE , EBD , are two right ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( Ax . 1. ) to one another ; therefore 4. The angles CBE , EBD , are equal to the angles DBA , ABC ; but CBE , EBD , are two right ...
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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