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 78
... chord AB ; then will AB be bisected in the point E. For join the points AD , DB , as before : Then , fince the angle DAB is equal to the angle DBA ( I. 5. ) , and the angle AED to the angle DEB , ( being each of them right angles ) the ...
... chord AB ; then will AB be bisected in the point E. For join the points AD , DB , as before : Then , fince the angle DAB is equal to the angle DBA ( I. 5. ) , and the angle AED to the angle DEB , ( being each of them right angles ) the ...
Side 79
... chord at right angles , it paffes through the centre of the circle ( III . 1. Cor . ) ; whence the centre must be fomewhere in the line FD . And , in the fame manner , it may be fhewn , that the centre must be somewhere in the line GE ...
... chord at right angles , it paffes through the centre of the circle ( III . 1. Cor . ) ; whence the centre must be fomewhere in the line FD . And , in the fame manner , it may be fhewn , that the centre must be somewhere in the line GE ...
Side 82
... abfurd . The point c , therefore , cannot be the centre of the circle BDF ; and the fame may be fhewn of any other point out of the line AF . Q. E. D. ) PRO P. VIII . THEOREM . Any two chords PROP . 82 ELEMENTS OF GEOMETRY .
... abfurd . The point c , therefore , cannot be the centre of the circle BDF ; and the fame may be fhewn of any other point out of the line AF . Q. E. D. ) PRO P. VIII . THEOREM . Any two chords PROP . 82 ELEMENTS OF GEOMETRY .
Side 83
... chords in a circle , which are equally distant from the centre , are equal tó each other ; and if they be equal to each ... chord , bifects it ( III . 3. ) , AC will be equal to CB , and DF to FE . And , because the angles ACO , DFO are ...
... chords in a circle , which are equally distant from the centre , are equal tó each other ; and if they be equal to each ... chord , bifects it ( III . 3. ) , AC will be equal to CB , and DF to FE . And , because the angles ACO , DFO are ...
Side 84
... chord AB be equal to the chord DE ; then will oc , of , or their diftances from the centre , be equal to each other . For the fquares of AC , CO are equal to the fquare of OA ( II . 14. ) , and the squares of DF , FO to the fquare of OD ...
... chord AB be equal to the chord DE ; then will oc , of , or their diftances from the centre , be equal to each other . For the fquares of AC , CO are equal to the fquare of OA ( II . 14. ) , and the squares of DF , FO to the fquare of OD ...
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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.