## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected : and Some of Euclid's Demonstrations Restored : Also the Book of Euclid's Data, in Like Manner CorrectedJ. Nourse, London, 1781 - 520 sider |

### Inni boken

Resultat 1-5 av 100

Side 16

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**wherefore**AL and BC are each of them equal to BG ; and things that are equal to the fame are equal to one another ; therefore the ftraight line AL is equal to BC .**Wherefore**from the given point A a ftraight line AL has been drawn equal ... Side 17

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**wherefore**alfo the point C fhall coincide with the point F , because the ftraight line AC is equal to DF : But the point B coincides with the point E ;**wherefore**the bafe BC fhall coincide with the bafe EF , because the point B ... Side 21

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**wherefore**likewife the angle BAC coincides with the angle EDF , and is equal to it . There- b . 8. Ax fore if two triangles , & c . Q. E. D. T PROP . IX . PRO B. O bifect a given rectilineal angle , that is , to divide it into two equal ... Side 25

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**Wherefore**, if at a point , & c . Q. E. D. PROP . XV . THEOR . IF two straight lines cut one another , the vertical , or op- pofite , angles fhall be equal . Let the two ftraight lines AB , CD cut one another in the point E ; the angle ... Side 33

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**wherefore**also the angle BCG is equal to the angle BCA , the lefs to the greater , which is impoffible ; therefore ...**wherefore**BC is not unequal to EF , that is , b 16. 1 . it is equal to it ; and AB is equal to DE ; therefore the two ...### Andre utgaver - Vis alle

The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |

### Vanlige uttrykk og setninger

alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fides BA fimilar fince firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC vertex wherefore