Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 Seiten |
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Seite 38
... Since , therefore , the right line AC interfects the two right lines AD , BC , and makes the alternate angles equal to each other , thofe lines will be parallel ( Prop.23 . ) But the line AD has been proved to be equal to the line BC ...
... Since , therefore , the right line AC interfects the two right lines AD , BC , and makes the alternate angles equal to each other , thofe lines will be parallel ( Prop.23 . ) But the line AD has been proved to be equal to the line BC ...
Seite 39
... inward oppofite angle BEC ( Prop . 25. ) Since , therefore , the angle ECB is equal to the angle FDA , and the angle AFD to the angle BEC , the remaining D 4 angle angle CBE will be equal to the remaining angle DAF BOOK 39 THE FIRST .
... inward oppofite angle BEC ( Prop . 25. ) Since , therefore , the angle ECB is equal to the angle FDA , and the angle AFD to the angle BEC , the remaining D 4 angle angle CBE will be equal to the remaining angle DAF BOOK 39 THE FIRST .
Seite 110
... Since , therefore , the rectangle under the fum and dif- ference of any two lines is equal to the difference of their fquares ( II . 13. ) , the rectangle of CG , CD will be equal to the difference of the fquares of CE , EA . But the ...
... Since , therefore , the rectangle under the fum and dif- ference of any two lines is equal to the difference of their fquares ( II . 13. ) , the rectangle of CG , CD will be equal to the difference of the fquares of CE , EA . But the ...
Seite 129
... Since , therefore , the triangles EFA , AGB , & c . are equiangular , and have their bafes EA , AB , & c . equal to each other , the remaining fides EF , FA , AG , GB , & c . will also be equal ( I. 21. ) : And fince LF , FG , & c . are ...
... Since , therefore , the triangles EFA , AGB , & c . are equiangular , and have their bafes EA , AB , & c . equal to each other , the remaining fides EF , FA , AG , GB , & c . will also be equal ( I. 21. ) : And fince LF , FG , & c . are ...
Seite 131
... Since , therefore , the angle OCD is equal to the angle ODC ( by Hyp . and Ax . 7. ) , the fide oc will also be equal to the fide OD ( I. 5. ) And , in the fame manner , it may be shewn , that OD , OE , OA , OB and oc are all equal to ...
... Since , therefore , the angle OCD is equal to the angle ODC ( by Hyp . and Ax . 7. ) , the fide oc will also be equal to the fide OD ( I. 5. ) And , in the fame manner , it may be shewn , that OD , OE , OA , OB and oc are all equal to ...
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Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.