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
... whole in the form of a synopsis which , it is hoped , the teacher will find of no small advantage in the important business of examination . This plan will , it is believed , give considerable aid to the student , in enabling him not ...
... whole in the form of a synopsis which , it is hoped , the teacher will find of no small advantage in the important business of examination . This plan will , it is believed , give considerable aid to the student , in enabling him not ...
Σελίδα 6
... whole is greater than its part . IX . X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meet two straight lines , so as to make the two interior angles on the same ...
... whole is greater than its part . IX . X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meet two straight lines , so as to make the two interior angles on the same ...
Σελίδα 9
... whole triangle ABC shall coincide with the whole triangle DEF and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . 6. The angle ABC shall be equal to ...
... whole triangle ABC shall coincide with the whole triangle DEF and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . 6. The angle ABC shall be equal to ...
Σελίδα 10
... whole AF is equal to the whole AG , of which the parts AB , AC are equal , ( Ax . 3. ) 3. The remainder BF shall be equal to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two ...
... whole AF is equal to the whole AG , of which the parts AB , AC are equal , ( Ax . 3. ) 3. The remainder BF shall be equal to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two ...
Σελίδα 31
... was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3. The whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to each of these equals add the angle ACB ; BOOK I. - PROP . XXXI . XXXII . 31.
... was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3. The whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to each of these equals add the angle ACB ; BOOK I. - PROP . XXXI . XXXII . 31.
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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