The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second Edition |
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Página 9
is impossible ; therefore 4 . The base BC shall coincide with the base EF , and ( Ax . 8. ) be equal to it . Wherefore also 5 . The whole triangle ABC shall coincide with the whole triangle DEF and be equal to it ; and the other angles ...
is impossible ; therefore 4 . The base BC shall coincide with the base EF , and ( Ax . 8. ) be equal to it . Wherefore also 5 . The whole triangle ABC shall coincide with the whole triangle DEF and be equal to it ; and the other angles ...
Página 12
The angle BDC is equal to the angle BCD ; but it has been 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 4C ...
The angle BDC is equal to the angle BCD ; but it has been 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 4C ...
Página 13
But this is impossible ( I. 7. ) ; therefore , if the base BC coincide with the base EF , the sides BA , AC , cannot but coincide with the sides ED , DF ; wherefore likewise 3 . The angle BAC coincides with the angle EDF , and is equal ...
But this is impossible ( I. 7. ) ; therefore , if the base BC coincide with the base EF , the sides BA , AC , cannot but coincide with the sides ED , DF ; wherefore likewise 3 . The angle BAC coincides with the angle EDF , and is equal ...
Página 15
The angle DBE is equal to the angle CBE , the less to the greater , which is impossible ; therefore 4 . Troo straight lines cannot have a common segment . PROP . XII .-- PROBLEM . To draw a straight BOOK I.PROP . XI . 15.
The angle DBE is equal to the angle CBE , the less to the greater , which is impossible ; therefore 4 . Troo straight lines cannot have a common segment . PROP . XII .-- PROBLEM . To draw a straight BOOK I.PROP . XI . 15.
Página 18
The remaining angle ABE is equal to the remaining angle ABD , the less to the greater , which is impossible ; therefore 4 . BE is not in the same straight line with BC . And in like manner it may be demonstrated that no other can be in ...
The remaining angle ABE is equal to the remaining angle ABD , the less to the greater , which is impossible ; therefore 4 . BE is not in the same straight line with BC . And in like manner it may be demonstrated that no other can be in ...
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AB is equal ABC is equal ABCD angle ABC angle ACB angle AGH angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line gnomon greater impossible inscribed join less Let ABC Let the straight likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC Take touches the circle triangle ABC twice the rectangle wherefore whole
Información bibliográfica
| Título | The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second Edition |
| Autores | EUCLID., Samuel A. GOOD |
| Edición | 2 |
| Editor | Charles Henry Law, 1854 |
| Procedencia del original | Biblioteca Británica |
| Digitalizado | 10 Dic. 2013 |
| Largo | 120 páginas |
| Exportar cita | BiBTeX EndNote RefMan |