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 |
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Página 46
but the triangle ABC is the half of the parallelogram EBCA , because the diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it ; and the halves of equal ...
but the triangle ABC is the half of the parallelogram EBCA , because the diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it ; and the halves of equal ...
Página 47
of the triangle ABC , because the diameter AC divides it into two equal parts ; whereB fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB , To describe a parallelogram that ...
of the triangle ABC , because the diameter AC divides it into two equal parts ; whereB fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB , To describe a parallelogram that ...
Página 48
The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another . > Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is ...
The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another . > Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is ...
Página 49
... and produce HA , GB to the points L , M : Then HLKF is a parallelogram , of which the diameter is HK , and AG , ME are the parallelograms about HK ; and LB , BF are the complements ; therefore LB is equal ( 43. 1. ) ...
... and produce HA , GB to the points L , M : Then HLKF is a parallelogram , of which the diameter is HK , and AG , ME are the parallelograms about HK ; and LB , BF are the complements ; therefore LB is equal ( 43. 1. ) ...
Página 56
From the demonstration , it is manifest that the parallelograms about the diameter of a square are likewise squares . PROP . V. THEOR . If a straight line be divided into two equal parts , and also into two ainequal parts ...
From the demonstration , it is manifest that the parallelograms about the diameter of a square are likewise squares . PROP . V. THEOR . If a straight line be divided into two equal parts , and also into two ainequal parts ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Información bibliográfica
| Título | 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 |
| Autor | John Playfair |
| Editor | E. Duyckinck, and George Long, 1824 |
| Procedencia del original | Universidad de Indiana |
| Digitalizado | 15 Ene. 2009 |
| Largo | 333 páginas |
| Exportar cita | BiBTeX EndNote RefMan |