## Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles |

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### Common terms and phrases

ABCD alſo given altitude baſe becauſe circle common compounded Cone conſequently Conſtr contained Coroll cube Demonſtr deſcribed diameter divided double draw drawn equal equilateral fall fame fide figure firſt fore fourth given by kind given by poſition given magnitude given reaſon greater hath Hence join leaſt leſs likewiſe line BC magnitude manner meaſure medial multiplied parallel parallelogram pentagone perpendicular plane prime produced PROP proportion pyramides rational reaſon rectangle remaining reſidual right angles right line ſaid ſame ſay ſecond ſeeing ſegment ſhall ſide ſolid ſpace ſphere ſquare ſuperficies Take taken thence thereof theſe things third thoſe touch triangle triangle ABC whence Wherefore whole whoſe

### Popular passages

Page 26 - 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 406 - ... which, when produced, the perpendicular falls, and the straight line intercepted, without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn...

Page 269 - A fphere is a folid figure defcribed by the revolution of a i'emicircle about its diameter, which remains unmoved. XV. The axis of a fphere is the fixed ftraight line about which the femicircle revolves. XVI. The centre of a fphere is the fame with that of the femicircle. XVII. The diameter of a fphere is any ftraight line which pafles through the centre, and is terminated both ways by the fuperficies of the fphere.

Page 2 - The radius of a circle is a right line drawn from the centre to the circumference.

Page 1 - Bounds) of a Line, are Points. IV. A Right Line, is that which lietb evenly between its Points.

Page 269 - ... be less than the other side, an obtuse angled ; and if greater, an acute angled cone. XIX. The axis of a cone is the fixed straight line about which the triangle revolves. XX. The base of a cone is the circle described by that side containing the right angle which revolves. XXI. A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed.

Page 26 - ... the fum of the remaining angles of the one triangle equal to the fum of the remaining angles of the other. 3 . If one angle in a triangle be right, the other two are equal to a right-angle.

Page 76 - ... the angular points of the figure about which it is defcribed, each thro' each. III. A rectilineal figure is faid to be infcribed in a circle, when all the angles of the infcribed figure are upon the circumference of the circle.

Page 77 - ... touch the circumference of the circle. IV A right-lined figure is faid to be defcribed about a circle, when all the fides of the figure which is circumfcribed touch the periphery of the circle V.

Page 269 - Right Lines that touch one another, and are •not in the fame Superficies: Or, a folid Angle is that which is contained under more than two plane Angles which are not in the fame Superficies, but being all at one Point.