Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of Euclid. With Notes, Critical and ExplanatoryJohnson, 1803 - 279 sider |
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Side 60
... difference . K H D E Let AB , AC be any two unequal lines ; then will the difference of the fquares of thofe lines be equal to a rect . angle under their fum and difference . For upon AB , AC make the fquares AE , AI ( II . 1. ) and in ...
... difference . K H D E Let AB , AC be any two unequal lines ; then will the difference of the fquares of thofe lines be equal to a rect . angle under their fum and difference . For upon AB , AC make the fquares AE , AI ( II . 1. ) and in ...
Side 61
... difference of AB and Ac . But the rectangle KG is contained by HG and HK , whence it is , alfo , contained by the fum and difference of AB and AC . And , fince LE is equal to HK ( I. 30. ) or CB ( by Conft . ) , and EG to AC ( by Conft ...
... difference of AB and Ac . But the rectangle KG is contained by HG and HK , whence it is , alfo , contained by the fum and difference of AB and AC . And , fince LE is equal to HK ( I. 30. ) or CB ( by Conft . ) , and EG to AC ( by Conft ...
Side 62
... . Q. E. D. COROLL . The difference of the fquares of the hypo- tenuse and either of the other fides is equal to the square of the remaining fide . PRO P. XV . THEOREM . If the fquare of PROP . 62 ELEMENTS OF GEOMETRY .
... . Q. E. D. COROLL . The difference of the fquares of the hypo- tenuse and either of the other fides is equal to the square of the remaining fide . PRO P. XV . THEOREM . If the fquare of PROP . 62 ELEMENTS OF GEOMETRY .
Side 64
... difference of the fquares of AC , CB be equal to the difference of the fquares of AD , DB . For the fum of the squares of AD , DC is equal to the fquare of AC ( II . 14. ) ; and the fum of the squares of BD , DC is equal to the fquare ...
... difference of the fquares of AC , CB be equal to the difference of the fquares of AD , DB . For the fum of the squares of AD , DC is equal to the fquare of AC ( II . 14. ) ; and the fum of the squares of BD , DC is equal to the fquare ...
Side 65
... difference of the fquares of AC , CB is equal to the difference of the fquares of Q.E.D. COROLL . The rectangle under the fum and difference of the two fides of any triangle , is equal to the rectangle under the base and the difference ...
... difference of the fquares of AC , CB is equal to the difference of the fquares of Q.E.D. COROLL . The rectangle under the fum and difference of the two fides of any triangle , is equal to the rectangle under the base and the difference ...
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Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
ABCD abfurd alfo equal alſo be equal alternate angle altitude angle ABC angle ACB angle AGH angle BAC angle CAB angle CBD angle DEF angle EGB bafe baſe becauſe bifect centre circle ABC circumference Conft COROLL demonftrated diagonal diſtance draw equal and parallel equal to BC equiangular equimultiples EUCLID fame manner fame multiple fame parallels fame ratio fection fegment fhewn fide AB fide BC fince the angles folid fome fquares of AC given right line interfect join the points lefs leſs Let ABC Let the right magnitudes muſt oppofite angle outward angle parallel right lines parallelogram parallelogram AC perpendicular polygon Prop propofition Q.E.D. PROP rectangle of AC remaining angle right angles right lines AB ſame SCHOLIUM ſquare ſtand taken THEOREM theſe thoſe three fides triangle ABC whence
Populære passager
Side 63 - 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 31 - THE Angle formed by a Tangent to a Circle, and a Chord drawn from the Point of Contact, is Equal to the Angle in the Alternate Segment.
Side xii - 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 xxiii - 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 63 - 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 24 - 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 i - 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 xii - The radius of a circle is a right line drawn from the centre to the circumference.
Side 30 - 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 7 - 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.