Elements of Geometry; Containing the First Six Books of Euclid ...For Bell & Bradfute, 1814 - 461 Seiten |
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Seite 17
... straight line . " COR . Hence two straight lines cannot inclose a space . " Neither can two straight lines have a common seg- " ment ; that is , they cannot coincide in part , without coinciding altogether . 66 " " IV . A superficies is ...
... straight line . " COR . Hence two straight lines cannot inclose a space . " Neither can two straight lines have a common seg- " ment ; that is , they cannot coincide in part , without coinciding altogether . 66 " " IV . A superficies is ...
Seite 18
... straight line between them lies wholly in that superficies . VI . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . A E B C N. B. When ...
... straight line between them lies wholly in that superficies . VI . A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . A E B C N. B. When ...
Seite 22
... straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be described from any centre , at any distance from ...
... straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be described from any centre , at any distance from ...
Seite 24
... line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , a 3. Postu- at the distance AB , de- late . scribe the circle BCD , and from ... straight lines DA , BD. 24 ELEMENTS.
... line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , a 3. Postu- at the distance AB , de- late . scribe the circle BCD , and from ... straight lines DA , BD. 24 ELEMENTS.
Seite 25
Euclid, John Playfair. F ; and produce the straight lines DA , BD , to E and F , from , the centre B , at the ... line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight ...
Euclid, John Playfair. F ; and produce the straight lines DA , BD , to E and F , from , the centre B , at the ... line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected Book centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles GEOMETRY given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB proportional 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 SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore