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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Resultat 1-5 av 17
Side 12
... shewn that it cannot be lefs ; confequently they are equal to each other . QE . D. COROL . Every equiangular triangle is also equi- lateral . PROP . VII . THEOREM . If the three fides PROP . 12 ELEMENTS OF GEOMETRY .
... shewn that it cannot be lefs ; confequently they are equal to each other . QE . D. COROL . Every equiangular triangle is also equi- lateral . PROP . VII . THEOREM . If the three fides PROP . 12 ELEMENTS OF GEOMETRY .
Side 62
... shewn to be equal ; whence the tri- angle ABF is equal to the triangle ACD ( I. 4. ) But the square AG is double the triangle ABF ( I. 32. ) · and the parallelogram AL is double the triangle ACD ( I 32. ) ; confequently the ...
... shewn to be equal ; whence the tri- angle ABF is equal to the triangle ACD ( I. 4. ) But the square AG is double the triangle ABF ( I. 32. ) · and the parallelogram AL is double the triangle ACD ( I 32. ) ; confequently the ...
Side 78
... shewn . COROLL . If a right line be drawn from the vertex of an ifofceles triangle , to the middle of the bafe , it will be perpendicular to it ; and if it be perpendicular to the base , it will bifect both it and the vertical angle ...
... shewn . COROLL . If a right line be drawn from the vertex of an ifofceles triangle , to the middle of the bafe , it will be perpendicular to it ; and if it be perpendicular to the base , it will bifect both it and the vertical angle ...
Side 81
... , which is impoffible . The point c , therefore , cannot be the centre of the circle BDF ; and the fame may be shewn of point out of the line AB . G any other Q.E. D. PROP . PROP . VII . THEOREM . If two circles touch BOOK THE THIRD . 81.
... , which is impoffible . The point c , therefore , cannot be the centre of the circle BDF ; and the fame may be shewn of point out of the line AB . G any other Q.E. D. PROP . PROP . VII . THEOREM . If two circles touch BOOK THE THIRD . 81.
Side 86
... EC . But fince EF is greater than EC , the point F will fall without the circle ABC ; and the fame may be shewn of any other point in BD , except B. The line BD , therefore , cannot cut the circle The 86 ELEMENTS OF GEOMETRY .
... EC . But fince EF is greater than EC , the point F will fall without the circle ABC ; and the fame may be shewn of any other point in BD , except B. The line BD , therefore , cannot cut the circle The 86 ELEMENTS OF GEOMETRY .
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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.