Euclid's Elements of Geometry, Bøker 1-6Henry Martyn Taylor The University Press, 1893 - 504 sider |
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Side viii
... called the postulates of geometrical operation , such as " it is assumed that a straight line may be drawn from any point to any other point , " but also geometrical theorems , the truth of which we assume , such as " two straight lines ...
... called the postulates of geometrical operation , such as " it is assumed that a straight line may be drawn from any point to any other point , " but also geometrical theorems , the truth of which we assume , such as " two straight lines ...
Side ix
... Propositions 5 and 6 of Book I. , and in Book II . The use of what may be called impossible figures , such as occurred in Euclid's text in the proofs of Propositions 6 and 7 of Book I. has been avoided . PREFACE . ix.
... Propositions 5 and 6 of Book I. , and in Book II . The use of what may be called impossible figures , such as occurred in Euclid's text in the proofs of Propositions 6 and 7 of Book I. has been avoided . PREFACE . ix.
Side x
... called in Trigonometry " the ambiguous case " in the solution of triangles . Another new Proposition ( 41 A ) is the solution of the problem " to construct a triangle equal to a given rectilineal figure . " It appears to be a more ...
... called in Trigonometry " the ambiguous case " in the solution of triangles . Another new Proposition ( 41 A ) is the solution of the problem " to construct a triangle equal to a given rectilineal figure . " It appears to be a more ...
Side xii
... introduce the student to this method and by a selection of exercises , which can readily be solved by its means , to indicate the importance of the method . The elegant theorem commonly called Ptolemy's Theorem is not found.
... introduce the student to this method and by a selection of exercises , which can readily be solved by its means , to indicate the importance of the method . The elegant theorem commonly called Ptolemy's Theorem is not found.
Side xii
Henry Martyn Taylor. The elegant theorem commonly called Ptolemy's Theorem is not found in Euclid's text . It was incorporated by Dr Robert Simson in one of his later editions as Pro- position D of Book VI . The position in those modern ...
Henry Martyn Taylor. The elegant theorem commonly called Ptolemy's Theorem is not found in Euclid's text . It was incorporated by Dr Robert Simson in one of his later editions as Pro- position D of Book VI . The position in those modern ...
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Vanlige uttrykk og setninger
ABCD AC is equal ADDITIONAL PROPOSITION angle ACB angle BAC angles ABC anharmonic arc ABC bisected centre of similitude chord circle ABC coincide Constr Coroll cut the circle describe a circle diagonal diameter draw equal angles equal circles equal to CD equiangular equimultiples Euclid EXERCISES exterior angle given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed intersect Let ABC meet middle points opposite sides pair parallel parallelogram pencil pentagon perpendicular polygon PROOF Prop PROPOSITION 14 Ptolemy's Theorem quadrilateral radical axis radius rectangle contained required to prove respectively rhombus right angles shew sides BC Similarly square on AC straight line &c straight line drawn straight line joining subtend tangent theorem triangle ABC triangle DEF triangles are equal twice the rectangle vertices Wherefore
Populære avsnitt
Side 59 - Any two sides of a triangle are together greater than the third side.
Side 7 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.
Side 68 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 144 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Side 376 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Side 135 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 305 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Side 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Side 248 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.