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 |
Fra bogen
Resultater 1-5 af 27
Side 137
... equimultiples , thefe will also be equi- multiples , the one of the fecònd , and the other of the fourth . E H B Let A the firft , be the fame multiple of в the second , as c the third , is of D the fourth ; and let EF and GH be ...
... equimultiples , thefe will also be equi- multiples , the one of the fecònd , and the other of the fourth . E H B Let A the firft , be the fame multiple of в the second , as c the third , is of D the fourth ; and let EF and GH be ...
Side 138
... equimultiples of the first and second may be taken , and fome multiple of the third fuch , that the former fhall be greater than that of the third , but the latter not greater . 1 L с K Б -A Di F Let AB , BC be two unequal magnitudes ...
... equimultiples of the first and second may be taken , and fome multiple of the third fuch , that the former fhall be greater than that of the third , but the latter not greater . 1 L с K Б -A Di F Let AB , BC be two unequal magnitudes ...
Side 139
... equimultiples GF , FE fuch , that they may be each greater than D ; and of D take the multiples K and L fuch , that ... equimulti- ples of the magnitudes AB and BC , and L is a multiple of D. And , fince GF is not lefs than K , and EF is ...
... equimultiples GF , FE fuch , that they may be each greater than D ; and of D take the multiples K and L fuch , that ... equimulti- ples of the magnitudes AB and BC , and L is a multiple of D. And , fince GF is not lefs than K , and EF is ...
Side 140
... equimultiples whatever of the antecedents will be proportional to any equimultiples whatever of the confequents . E- P F A Br G D H M any Let A be to B as C is to D , and of A and C take equimultiples EK , FL ; and of B and D any ...
... equimultiples whatever of the antecedents will be proportional to any equimultiples whatever of the confequents . E- P F A Br G D H M any Let A be to B as C is to D , and of A and C take equimultiples EK , FL ; and of B and D any ...
Side 141
... equimultiples whatever of GM , HN ; EK will have the fame ratio to GM , that FL has to HN ( V. Def . 5. ) Q.E.D. ... equimultiples E and G , and of B and D the fame equimultiples F and H. Then , because A is to B , as C is to D ( by Hyp ...
... equimultiples whatever of GM , HN ; EK will have the fame ratio to GM , that FL has to HN ( V. Def . 5. ) Q.E.D. ... equimultiples E and G , and of B and D the fame equimultiples F and H. Then , because A is to B , as C is to D ( by Hyp ...
Andre udgaver - Se alle
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.