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 100
Side 7
... alfo equal to the part DB ( Def . 16. ) , whence the remainder AG will be equal to the remainder BF ( Ax . 3. ) And fince AG , BC have been each proved to be equal to BF , AG will alfo be equal to BC ( Ax . 1. ) A right line AG , has ...
... alfo equal to the part DB ( Def . 16. ) , whence the remainder AG will be equal to the remainder BF ( Ax . 3. ) And fince AG , BC have been each proved to be equal to BF , AG will alfo be equal to BC ( Ax . 1. ) A right line AG , has ...
Side 8
... alfo equal to the part DB ( Def . 16. ) , whence the remainder AG will be equal to the remainder BF ( Ax . 3. ) And fince AG , BC have been each proved to be equal to BF , AG will also be equal to BC ( Ax . 1. ) A right line AG , has ...
... alfo equal to the part DB ( Def . 16. ) , whence the remainder AG will be equal to the remainder BF ( Ax . 3. ) And fince AG , BC have been each proved to be equal to BF , AG will also be equal to BC ( Ax . 1. ) A right line AG , has ...
Side 11
... alfo be equal to the fide BD , the angle CAE to the angle CBD , and the angle D to the angle E ( Prop . 4. ) And fince the whole CD is equal to the whole CE ( by Conft . ) , and the part CA to the part CB ( by Hyp . ) , the remaining ...
... alfo be equal to the fide BD , the angle CAE to the angle CBD , and the angle D to the angle E ( Prop . 4. ) And fince the whole CD is equal to the whole CE ( by Conft . ) , and the part CA to the part CB ( by Hyp . ) , the remaining ...
Side 14
... alfo , be equal to the corresponding angles of the triangle Acb . Q. E.D. PROP . VIII . THEOREM . All right angles are equal to each other . G E Let ABC , DEF be each of them right angles ; then will ABC be equal to DEF . For conceive ...
... alfo , be equal to the corresponding angles of the triangle Acb . Q. E.D. PROP . VIII . THEOREM . All right angles are equal to each other . G E Let ABC , DEF be each of them right angles ; then will ABC be equal to DEF . For conceive ...
Side 17
... alfo , be equal to the angle FDC ( Prop . 7. ) But one right line is perpendicular to another when the angles on both fides of it are equal ( Def . 8. ) ; there- fore CD is perpendicular to AB ; and it is drawn from the point D as was ...
... alfo , be equal to the angle FDC ( Prop . 7. ) But one right line is perpendicular to another when the angles on both fides of it are equal ( Def . 8. ) ; there- fore CD is perpendicular to AB ; and it is drawn from the point D as was ...
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.