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 |
Inni boken
Side 11
... one of them is greater than the other : Let AB be the greater , and from it cut off
DB equal to AC the less , and join DC ; therefore , because in the triangles DBC ,
D ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are ...
... one of them is greater than the other : Let AB be the greater , and from it cut off
DB equal to AC the less , and join DC ; therefore , because in the triangles DBC ,
D ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are ...
Side 14
Join B and E the middle point of the line AC , and produce BE to F , А. and make
EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC ,
and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle E AEB
...
Join B and E the middle point of the line AC , and produce BE to F , А. and make
EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC ,
and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle E AEB
...
Side 15
A AB ; the angle ABC is also greater than the angle BCA . Make AD equal to AB ,
and join BD : and because ADB is the exterior angle of the triangle BDC , it is
greater ( 9. 1. ) D than the interior and opposite angle DCB ; but ADB is equal ( 3.
1. ) ...
A AB ; the angle ABC is also greater than the angle BCA . Make AD equal to AB ,
and join BD : and because ADB is the exterior angle of the triangle BDC , it is
greater ( 9. 1. ) D than the interior and opposite angle DCB ; but ADB is equal ( 3.
1. ) ...
Side 17
EDG equal to the angle BAC : and make DG equal to AC or DF , and join EG , GF
Because AB is equal А D to DE , and AC to DG , the two sides BA , AC are equal
to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG
...
EDG equal to the angle BAC : and make DG equal to AC or DF , and join EG , GF
Because AB is equal А D to DE , and AC to DG , the two sides BA , AC are equal
to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG
...
Side 18
Their equality would be manifest , if the third sides BC and EF were equal . If
possible , suppose that those sides are not equal , and that BC is the greater .
Take BH = EF ; and join AH . The triangle ABH = DEF ; for the right angles B and
E are ...
Their equality would be manifest , if the third sides BC and EF were equal . If
possible , suppose that those sides are not equal , and that BC is the greater .
Take BH = EF ; and join AH . The triangle ABH = DEF ; for the right angles B and
E are ...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |
Vanlige uttrykk og setninger
ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid spherical square straight line taken tangent THEOR third touch triangle ABC wherefore whole
Bibliografisk informasjon
| Tittel | 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 |
| Forfatter | John Playfair |
| Utgave | 6 |
| Utgiver | W. E. Dean, 1836 |
| Lengde | 311 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |