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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Side 156
... E together . Q. E. D. SCHOLIUM . That F muft be the leaft of the four mag- nitudes when A is the greateft , appears from propofitions VI . and XIII . воок VI . DEFINITIONS . 1. Similar rectilineal figures , BOOK 156 ELEMENTS OF GEOMETRY .
... E together . Q. E. D. SCHOLIUM . That F muft be the leaft of the four mag- nitudes when A is the greateft , appears from propofitions VI . and XIII . воок VI . DEFINITIONS . 1. Similar rectilineal figures , BOOK 156 ELEMENTS OF GEOMETRY .
Side 157
... Similar rectilineal figures , are those which are equi- angular , and have the fides about the equal angles pro- portional . 2. The homologous , or like fides , of fimilar figures , are those which are oppofite to equal angles . 3. Two ...
... Similar rectilineal figures , are those which are equi- angular , and have the fides about the equal angles pro- portional . 2. The homologous , or like fides , of fimilar figures , are those which are oppofite to equal angles . 3. Two ...
Side 180
... double the triangle DME , the triangle ABC will be to the triangle DEF as the fquare AL is to the fquare DN ( V. 13 and 15. ) Q. E. D. PRO P. XVII . THEOREM . Similar polygons are to PROP , 189 ELEMENTS OF GEOMETRY .
... double the triangle DME , the triangle ABC will be to the triangle DEF as the fquare AL is to the fquare DN ( V. 13 and 15. ) Q. E. D. PRO P. XVII . THEOREM . Similar polygons are to PROP , 189 ELEMENTS OF GEOMETRY .
Side 181
... Similar polygons are to each other as the fquares of their homologous fides . E H Let ABCDE , FGHIK be fimilar polygons , of which AB , G are homologous fides ; then will the polygon ABCDE be to the polygon FGHIK as the square of AB is ...
... Similar polygons are to each other as the fquares of their homologous fides . E H Let ABCDE , FGHIK be fimilar polygons , of which AB , G are homologous fides ; then will the polygon ABCDE be to the polygon FGHIK as the square of AB is ...
Side 214
... Similar folids , contained by plane figures , are such as have all their folid angles equal , each to each , and are bounded by the fame number of fimilar planes . 3. A prifm is a folid whofe ends are parallel , equal , and like plane ...
... Similar folids , contained by plane figures , are such as have all their folid angles equal , each to each , and are bounded by the fame number of fimilar planes . 3. A prifm is a folid whofe ends are parallel , equal , and like plane ...
Andre utgaver - Vis alle
Elements of Geometry: Containing the Principal Propositions in the First Six ... John Bonnycastle Uten tilgangsbegrensning - 1803 |
Elements of Geometry: Containing the Principal Propositions in the First Six ... John Bonnycastle Uten tilgangsbegrensning - 1803 |
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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 avsnitt
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.