Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and Explanatory
Johnson, 1803 - 279 sider
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Elements of Geometry: Containing the Principal Propositions in the First Six ...
Uten tilgangsbegrensning - 1803
abcd ac is equal angle abc angle acb angle bac angle cab angle cba base and altitude bisect Book centre chord circle abc circumserence consequently the angle Const Coroll demonstration diagonal diameter draw drawn equal and parallel equal angles equal bases equal to ac equi equiangular Euclid faid fame base fame manner fame multiple fame plane fame ratio fame right line fides given circle given right line greater inscribed intersect join the points klmn less Let abc Let the right opposite angles outward angle parallelepipedons parallelogram perpendicular point f polygon prism proportional proposition Q.E.D. PROP radii rectangle of ac remaining angle right angles Scholium segment shewn side ac sigure sirst solid square of ac taken tangent Theorem triangle abc triangle def twice the rectangle
Side 215 - AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length to become greater than AB.
Side 75 - To find the centre of a given circle. Let ABC be the given circle ; it is required to find its centre. Draw within it any straight line AB, and bisect (I.
Side 18 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Side 215 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Side 116 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw* the straight line GAH touching the circle in the a 17. 3. point A, and at the point A, in the straight line AH, makeb b 23.
Side iii - ELEMENTS of GEOMETRY, containing the principal Propositions in the first Six and the Eleventh and Twelfth Books of Euclid, with Critical Notes ; and an Appendix, containing various particulars relating to the higher part* of the Sciences.
Side 73 - The radius of a circle is a right line drawn from the centre to the circumference.
Side 102 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Side 35 - Beciprocally, when these properties exist for 'two right lines and a common secant, the two lines are parallel.* — Through a given point, to draw a right line parallel to a given right line, or cutting it at a given angle, — Equality of angles having their sides parallel and their openings placed in the same direction.