## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |

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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2016 |

### Common terms and phrases

alſo angle B A becauſe the angle biſected caſe centre circle A B circumference circumſcribed cone conſequent cylinder D E F demonſtrated deſcribed diameter equal angles equiangular equimultiples Euclid fides firſt given circle given right line given triangle greater inſcribed join leſs leſſer magnitudes oppoſite P R O B parallel parallelogram paſſing thro perpendicular point F polygon priſms prop proportional propoſition pyramid reëtangle remaining angle right angles right line A B right lined figure right-lined ſaid ſame altitude ſame multiple ſame ratio ſame reaſon ſay ſecond ſegment ſemidiameter ſhall ſides A B ſimilar ſince ſolid angle ſome ſphere ſtand ſuch ſum ſuperficies T H E O theſe thoſe trapezium triangle A B twice the ſquare uſe vertex the point Wherefore whoſe baſe

### Popular passages

Page 247 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Page 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.

Page 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

Page 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.

Page 56 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 391 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...

Page 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Page 130 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 183 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...