Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 sider |
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Resultater 1-5 af 21
Side 6
... double of the fame thing are equal to each other . 7. Things which are halves of the fame thing are equal to each other . 8. The whole is equal to all its parts taken together . 9. Magnitudes which coincide , or fill the fame space ...
... double of the fame thing are equal to each other . 7. Things which are halves of the fame thing are equal to each other . 8. The whole is equal to all its parts taken together . 9. Magnitudes which coincide , or fill the fame space ...
Side 41
... double the triangle . Let the parallelogram AC and the triangle AEB ftand upon the same base AB , and between the fame parallels AB , DE ; then will the parallelogram AC be double the triangle AEB . For join the points B , D ; then will ...
... double the triangle . Let the parallelogram AC and the triangle AEB ftand upon the same base AB , and between the fame parallels AB , DE ; then will the parallelogram AC be double the triangle AEB . For join the points B , D ; then will ...
Side 43
... double of DE ( by Conft . ) ; confequently AB is also the double of DE ; that is DE is the half of AB . 9 Q. E. D. PROP . PRO P. XXXV . PROBLEM . To divide a given BOOK THE FIRST . 43.
... double of DE ( by Conft . ) ; confequently AB is also the double of DE ; that is DE is the half of AB . 9 Q. E. D. PROP . PRO P. XXXV . PROBLEM . To divide a given BOOK THE FIRST . 43.
Side 50
... double the triangle BCA , and the fquare FH is double the triangle FGE ( I. 30. ) , the fquare BD will also be greater than the square FH . Again , let the fquare BD be greater than the square FH ; then will the fide AB be greater than ...
... double the triangle BCA , and the fquare FH is double the triangle FGE ( I. 30. ) , the fquare BD will also be greater than the square FH . Again , let the fquare BD be greater than the square FH ; then will the fide AB be greater than ...
Side 59
... doubles of equals are equal , the gnomon HBF , together with CK , will be the double of AK . But CK is a square upon CB ( II . 7. ) , and twice the rectangle AB , BC is the double of AK , whence the gno- mon HBF , together with the ...
... doubles of equals are equal , the gnomon HBF , together with CK , will be the double of AK . But CK is a square upon CB ( II . 7. ) , and twice the rectangle AB , BC is the double of AK , whence the gno- mon HBF , together with the ...
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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 BAC angle CAB angle DAF bafe baſe becauſe bifect cafe centre chord circle ABC circumference Conft 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 folid fome fquares of AC ftand given circle given right line infcribed interfect join the points lefs leſs Let ABC magnitudes muſt oppofite angles outward angle parallelepipedons parallelogram perpendicular polygon prifm propofition proportional Q. E. D. PROP reafon rectangle of AB rectangle of AC remaining angle right angles SCHOLIUM ſhall ſpace ſquare tangent THEOREM theſe thofe thoſe triangle ABC twice the rectangle whence
Populære passager
Side 166 - 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 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 215 - 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 117 - 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 point A (III. 17), and at the point A, in the straight line AH, make the angle HAG equal to the angle DEF (I.
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 249 - 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 102 - 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 i - Handbook to the First London BA Examination. Lie (Jonas). SECOND SIGHT; OR, SKETCHES FROM NORDLAND. By JONAS LIE. Translated from the Norwegian. [/» preparation. Euclid. THE ENUNCIATIONS AND COROLLARIES of the Propositions in the First Six and the Eleventh and Twelfth Books of Euclid's Elements.
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.
Side 145 - 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.