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

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### Common terms and phrases

ABCD alſo given altitude baſe becauſe circle common compounded Cone conftr conſequently contained Coroll cube demonſtrated deſcribed diameter divided Dodecaedron double draw drawn equal equilateral fall fame fide figure firſt folid fore four fourth given in kind given in poſition given Magnitude given ratio greater Hence inſcribed join leſs likewiſe line AC magnitude manner meaſure medial multiplied parallel parallelogram pentagone perpendicular plane prime produced PROP proportion ratio rectangle remaining reſidual right angles right line right-line ſaid ſame ſay ſecond ſeeing ſegment ſhall ſide ſolid ſpace ſphere ſquare ſuperficies Take taken thence thereof theſe third thoſe triangle ABC whence Wherefore whole whoſe

### Popular passages

Page 120 - An EVEN NUMBER is that which can be divided into two equal whole numbers.

Page 325 - ... 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 46 - Hence, a right line drawn from the extremity of the .diameter of a circle, and at right -angles, is a tangent to the faid circle. From this propofition are gathered many paradoxes, and wonderful confecbtries, which you may meet with in the interpreters.

Page 248 - Right-lined plane Angles equal , from whofe Points equal Right Lines be elevated on the Planes of the Angles, containing equal Angles with the Lines firft given, each to each ; Perpendiculars drawn from the extreme Points of thofe elevated Lines to the Planes of the Angles firft given, are equal to one another.

Page 174 - Divide KM into as many equal parts as there are units in the number B, and let as many of thefe, as there are units in the number C, b make the right line HR, it is manifeft that KM.

Page 61 - A circle is faid to be defcribcd about a figure when the periphery of the circle touches all the angles of the figure, which it circumfcribes. VII. A right line is faid to be fitted or applied in a circle when the extremes thereof fall upon the circumference; as the right line AB.

Page 20 - DBCF, becaufe they are upon the fame bafe BC, and between the fame parallels BC, EF ; and the triangle ABC is the half of the parallelogram EBCA...

Page 73 - A ; and here note, that the quantity which is referred to another quantity, is called the antecedent of the ratio ; and that to which the other is referred is called the consequent of the ratio ; as, in the ratio of A to B, A is the antecedent, and B the consequent.

Page 230 - Diameter of a fphere, is a right line drawn thro' the center, and terminated on either fide in the fuperficies of the fphere. XVIII. A Cone is a figure made, when one fide of a rectangled triangle ( v'fz.