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 7
... given lines are fo fitu- ate , that one of the extremities of c falls in the point A , the former part of the construction becomes un- neceffary . PROP . attention have been bestowed upon the work ; and that BOOK THE FIRST . 9.
... given lines are fo fitu- ate , that one of the extremities of c falls in the point A , the former part of the construction becomes un- neceffary . PROP . attention have been bestowed upon the work ; and that BOOK THE FIRST . 9.
Side 9
... SCHOLIUM . When the two given lines are fo fitu- ate , that one of the extremities of c falls in the point A , the former part of the construction becomes un- neceffary . PROP . PRO P. IV . THEOREM . If two fides and BOOK THE FIRST . 9.
... SCHOLIUM . When the two given lines are fo fitu- ate , that one of the extremities of c falls in the point A , the former part of the construction becomes un- neceffary . PROP . PRO P. IV . THEOREM . If two fides and BOOK THE FIRST . 9.
Side 10
... fall upon the point D , and the point B upon the point E. But right lines , which have the fame extremities , must coincide , or otherwife their parts would not lie in the fame direction , which is abfurd ( Def . 5. ) ; therefore ab falls ...
... fall upon the point D , and the point B upon the point E. But right lines , which have the fame extremities , must coincide , or otherwife their parts would not lie in the fame direction , which is abfurd ( Def . 5. ) ; therefore ab falls ...
Side 13
... fall at G ; and join CG . Then , fince the fide AC is equal to the fide DF , or AC ( by Hyp . ) , the angle ACG will be equal to the angle ACC ( Prop . 5. ) And , because the fide BC is equal to the fide EF , or BG ( by Hyp . ) , the ...
... fall at G ; and join CG . Then , fince the fide AC is equal to the fide DF , or AC ( by Hyp . ) , the angle ACG will be equal to the angle ACC ( Prop . 5. ) And , because the fide BC is equal to the fide EF , or BG ( by Hyp . ) , the ...
Side 14
... fall , if poffible , without the angle ABC , in the direction BG ; and produce AB to H .. Then , because the angles ABC , ABG are right angles ( by Hyp . ) , the lines CB , GB will be each perpendicular to AH ( Def . 8. 9. ) And , fince ...
... fall , if poffible , without the angle ABC , in the direction BG ; and produce AB to H .. Then , because the angles ABC , ABG are right angles ( by Hyp . ) , the lines CB , GB will be each perpendicular to AH ( Def . 8. 9. ) And , fince ...
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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.