# 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

Daniel Midwinter and Aaron Ward, 1732 - Euclid's Elements - 514 pages
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### 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.