Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα xiv
... proved . Indeed those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to shew its necessary ...
... proved . Indeed those who make the objection just stated , do not seem to have reflected sufficiently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to shew its necessary ...
Σελίδα 22
... proved that C A is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1 . Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB CB are equal to one ...
... proved that C A is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1 . Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB CB are equal to one ...
Σελίδα 24
... to the angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC ; the remain- der BF shall be equal ( 3. Ax . ) to the D T B G 1 2 2 C 6 remainder CG ; and FC was proved to be equal 24 ELEMENTS.
... to the angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC ; the remain- der BF shall be equal ( 3. Ax . ) to the D T B G 1 2 2 C 6 remainder CG ; and FC was proved to be equal 24 ELEMENTS.
Σελίδα 25
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles ...
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles ...
Σελίδα 26
... proved to be greater than the same BCD ; which is impossi- ble . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
... proved to be greater than the same BCD ; which is impossi- ble . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
| Συγγραφέας | John Playfair |
| Εκδότης | E. Duyckinck, and George Long, 1824 |
| Πρωτότυπο από | Πανεπιστήμιο της Ιντιάνα |
| Ψηφιοποιήθηκε στις | 15 Ιαν. 2009 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |