Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 páginas |
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Página 93
... two right angles . Let ABCD be a quadrilateral , infcribed in the circle ADCB ; then will the oppofite angles BAD , BCD , taken together , be equal to two right angles . For , For , draw the diagonals AC , BD , and -BOOK 93 THE THIRD .
... two right angles . Let ABCD be a quadrilateral , infcribed in the circle ADCB ; then will the oppofite angles BAD , BCD , taken together , be equal to two right angles . For , For , draw the diagonals AC , BD , and -BOOK 93 THE THIRD .
Página 94
... COROLL . If any fide AB , of the quadrilateral ABCD , be produced , the outward angle EAD will be equal to the inward oppofite angle BCD . PROP . XVIII . PROBLEM . Through any three points PROP . 94 ELEMENTS OF GEOMETRY .
... COROLL . If any fide AB , of the quadrilateral ABCD , be produced , the outward angle EAD will be equal to the inward oppofite angle BCD . PROP . XVIII . PROBLEM . Through any three points PROP . 94 ELEMENTS OF GEOMETRY .
Página 96
... ABCD be a quadrilateral , whofe oppofite angles DCB , DAB are , together , equal to two right angles : then may a circle be described about that quadrilateral . For fince the circumference of a circle may be de- scribed through any ...
... ABCD be a quadrilateral , whofe oppofite angles DCB , DAB are , together , equal to two right angles : then may a circle be described about that quadrilateral . For fince the circumference of a circle may be de- scribed through any ...
Página 97
... ABCD , as was to be fhewn . PRO P. XX . THEOREM . Segments of circles , which ftand upon equal chords , and contain equal angles , are equal to each other . Let ACB , DFE be two segments of circles , which stand upon the equal chords AB ...
... ABCD , as was to be fhewn . PRO P. XX . THEOREM . Segments of circles , which ftand upon equal chords , and contain equal angles , are equal to each other . Let ACB , DFE be two segments of circles , which stand upon the equal chords AB ...
Página 120
... ABCD be the given circle ; it is required to in- scribe a square in it . Through E , the centre of the circle , draw any two diameters AC , BD at right angles to each other ( I. 11 , 12. ) , and join AB , BC , CD and DA ; then will BCDA ...
... ABCD be the given circle ; it is required to in- scribe a square in it . Through E , the centre of the circle , draw any two diameters AC , BD at right angles to each other ( I. 11 , 12. ) , and join AB , BC , CD and DA ; then will BCDA ...
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Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.