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 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 7
... describe the circle BCD ( Pof . 3. ) And from the point B , at the distance BA , describe the circle ACE ( Pof . 3. ) Then , because the two circles pass through each other's centres , they will cut each other . And , if the right lines ...
... describe the circle BCD ( Pof . 3. ) And from the point B , at the distance BA , describe the circle ACE ( Pof . 3. ) Then , because the two circles pass through each other's centres , they will cut each other . And , if the right lines ...
Σελίδα 7
... describe the circle ACE ( Pof . 3. ) ... Then , because the two circles pass through each other's centres , they will cut each other . And , if the right lines CA , CB be drawn from the point of interfection C , ABC will be the ...
... describe the circle ACE ( Pof . 3. ) ... Then , because the two circles pass through each other's centres , they will cut each other . And , if the right lines CA , CB be drawn from the point of interfection C , ABC will be the ...
Σελίδα 7
... describe the cir- cle CEF ( Pof . 3. ) cutting DB produced in F. And from the point D , at the distance DF , defcribe the circle FHG ( Pof . 3. ) ; then , if DA be produced to G , AG will be equal to BC , as was required . For , fince B ...
... describe the cir- cle CEF ( Pof . 3. ) cutting DB produced in F. And from the point D , at the distance DF , defcribe the circle FHG ( Pof . 3. ) ; then , if DA be produced to G , AG will be equal to BC , as was required . For , fince B ...
Σελίδα 8
... describe the circle FHG ( Pof . 3. ) ; then , if DA be produced to a ,. AG will be equal to BC , as was required . For , fince B is the centre of the circle CEF , BC is equal to BF ( Def . 13. ) And , because D is the centre of the ...
... describe the circle FHG ( Pof . 3. ) ; then , if DA be produced to a ,. AG will be equal to BC , as was required . For , fince B is the centre of the circle CEF , BC is equal to BF ( Def . 13. ) And , because D is the centre of the ...
Σελίδα 15
... describe the equilateral triangle DFE ( Prop . 1. ) , and join AF ; then will AF bifect the angle BAC , as was required . For AD is equal to AE , by conftruction ; DF is alfo equal to FE ( Def . 16. ) , and AF is common to each of the ...
... describe the equilateral triangle DFE ( Prop . 1. ) , and join AF ; then will AF bifect the angle BAC , as was required . For AD is equal to AE , by conftruction ; DF is alfo equal to FE ( Def . 16. ) , and AF is common to each of the ...
Περιεχόμενα
63 | |
83 | |
90 | |
95 | |
111 | |
125 | |
189 | |
190 | |
33 | |
35 | |
23 | |
24 | |
29 | |
33 | |
21 | |
25 | |
37 | |
45 | |
47 | |
193 | |
194 | |
195 | |
199 | |
199 | |
199 | |
212 | |
221 | |
234 | |
242 | |
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα xii - The radius of a circle is a right line drawn from the centre to the circumference.
Σελίδα 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.
Σελίδα 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.