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 |
Dentro del libro
Resultados 1-5 de 24
Página 28
If a straight line , falling upon two other straight lines , make the alternate angles equal to one another , these two straight lines shall be parallel , Let the straight line EF , which falls upon the two straight lines AB , CD , make ...
If a straight line , falling upon two other straight lines , make the alternate angles equal to one another , these two straight lines shall be parallel , Let the straight line EF , which falls upon the two straight lines AB , CD , make ...
Página 29
3 . AB is parallel to CD . Wherefore if a straight line , & c . Q.E.D. PROP . XXIX . - THEOREM . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle ...
3 . AB is parallel to CD . Wherefore if a straight line , & c . Q.E.D. PROP . XXIX . - THEOREM . If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle ...
Página 30
but those straight lines which , with another straight line falling upon them , make the interior angles on the same side less than two right angles , will meet ( Ax . 12. ) together if continually produced ; therefore 3 .
but those straight lines which , with another straight line falling upon them , make the interior angles on the same side less than two right angles , will meet ( Ax . 12. ) together if continually produced ; therefore 3 .
Página 31
Again , because AB is parallel to CE , and BD falls upon them , 2 . The exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3 .
Again , because AB is parallel to CE , and BD falls upon them , 2 . The exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3 .
Página 41
Then because the straight line HF falls upon the parallels AH , EF , ( I. 29. ) 1 . The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9. ) 2 .
Then because the straight line HF falls upon the parallels AH , EF , ( I. 29. ) 1 . The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9. ) 2 .
Comentarios de la gente - Escribir un comentario
No encontramos ningún comentario en los lugares habituales.
Otras ediciones - Ver todas
Términos y frases comunes
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 |