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
... because the two circles pafs 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 equilateral triangle re- quired . For , fince A is the ...
... because the two circles pafs 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 equilateral triangle re- quired . For , fince A is the ...
Side 8
... because p is the centre of the circle FHG , DG is equal to DF ( Def . 13. ) But the part DA is 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 ...
... because p is the centre of the circle FHG , DG is equal to DF ( Def . 13. ) But the part DA is 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 ...
Side 10
... because CA coincides with FD , and the angle c is equal to the angle F ( by Hyp . ) , the fide CB will also coincide with the fide FE . And , fince CA is equal to FD , and CB to FE ( by Hyp . ) , the point A will fall upon the point D ...
... because CA coincides with FD , and the angle c is equal to the angle F ( by Hyp . ) , the fide CB will also coincide with the fide FE . And , fince CA is equal to FD , and CB to FE ( by Hyp . ) , the point A will fall upon the point D ...
Side 11
... because the two fides CA , CE of the triangle CAE , are equal to the two fides CB , CD of the triangle CBD , and the angle c is common , the fide AE will also be equal to the fide BD , the angle CAE to the angle CBD , and the angle D to ...
... because the two fides CA , CE of the triangle CAE , are equal to the two fides CB , CD of the triangle CBD , and the angle c is common , the fide AE will also be equal to the fide BD , the angle CAE to the angle CBD , and the angle D to ...
Side 13
... because the fide BC is equal to the fide EF , or BG ( by Hyp . ) , the angle BCG will be equal to the angle BGC ( Prop . 5. ) But fince the angles ACG , BCG are equal to the angles AGC , BGC , each to each , the whole angle ACB will be ...
... because the fide BC is equal to the fide EF , or BG ( by Hyp . ) , the angle BCG will be equal to the angle BGC ( Prop . 5. ) But fince the angles ACG , BCG are equal to the angles AGC , BGC , each to each , the whole angle ACB will be ...
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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 AC is equal alfo equal alſo be equal alſo be greater altitude angle ABC angle ACB angle BAD angle CAB bafe baſe becauſe bifect cafe centre chord circle ABC circumference confequently Conft COROLL DABC defcribe demonftration diagonal diameter diſtance draw EFGH equiangular equimultiples EUCLID fame manner fame multiple fame plane fame ratio fecond fection fegment fhewn fide AB fide AC fimilar fince the angles firſt folid fome fquares of AC given circle given right line infcribe interfect join the points lefs leſs Let ABC magnitudes muſt oppofite angles outward angle parallelogram perpendicular polygon prifm propofition proportional Q. E. D. PROP reaſon rectangle of AB rectangle of AE remaining angle right angles ſame SCHOLIUM ſhewn ſpace ſquare tangent THEOREM theſe triangle ABC twice the rectangle uſeful whence
Populære passager
Side 164 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 71 - The radius of a circle is a right line drawn from the centre to the circumference.
Side 69 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 205 - 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 18 - 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 239 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 5 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.
Side 133 - If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first of the sum of all the rest.
Side 143 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.
Side 155 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order.