## 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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Side

... wherever it had been corrupted , but in some cases removed imperfections that

probably belonged to the original work : though his extreme partiality for his

author never permitted him to suppose that such honour could

either ...

... wherever it had been corrupted , but in some cases removed imperfections that

probably belonged to the original work : though his extreme partiality for his

author never permitted him to suppose that such honour could

**fall**to the shareeither ...

Side 9

the side BA must

is equal to the angle F , the side AC must

occurring at the same time in the two straight lines 2 OF GEOMETRY . BOOK I.

the side BA must

**fall**on the side ED ; and , in like manner , because the angle Cis equal to the angle F , the side AC must

**fall**on the side DF . Hence , the point A ,occurring at the same time in the two straight lines 2 OF GEOMETRY . BOOK I.

Side 10

occurring at the same time in the two straight lines ED and FD , must

intersection D ; consequently , the two triangles BAC , EDF , are identical , or

mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles these three ...

occurring at the same time in the two straight lines ED and FD , must

**fall**on theirintersection D ; consequently , the two triangles BAC , EDF , are identical , or

mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles these three ...

Side 19

A If a straight line

equal to one another , these two straight lines are parallel . Let the straight line

EF , which

AEF ...

A If a straight line

**falling**upon two other straight lines makes the alternate anglesequal to one another , these two straight lines are parallel . Let the straight line

EF , which

**falls**upon the two straight lines AB , CD make the alternate anglesAEF ...

Side 20

Cor . Hence , when two straight lines are perpendicular to a third line , they will

be parallel to each other . PROP . XXI . THEOR . GHD ; If a straight line

two parallel straight lines , it makes the alternate angles equal to one another ;

and ...

Cor . Hence , when two straight lines are perpendicular to a third line , they will

be parallel to each other . PROP . XXI . THEOR . GHD ; If a straight line

**fall**upontwo parallel straight lines , it makes the alternate angles equal to one another ;

and ...

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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 - 1824 |

### 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 square straight line taken tangent THEOR third touch triangle ABC wherefore whole