Euclid's Elements of Geometry, Bøker 1-6;Bok 11Henry Martyn Taylor The University Press, 1895 - 657 sider |
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Side viii
... 5 and of every other Proposition , in which the theorem of Proposition 4 is quoted . It seems therefore but a slight alteration to adopt the direct use of this method in the proofs of any theorems , in the proofs of which viii PREFACE .
... 5 and of every other Proposition , in which the theorem of Proposition 4 is quoted . It seems therefore but a slight alteration to adopt the direct use of this method in the proofs of any theorems , in the proofs of which viii PREFACE .
Side ix
Henry Martyn Taylor. proofs of any theorems , in the proofs of which , in Euclid's text , the theorem of Proposition 4 is quoted . It may of course be fairly objected that it would be more logical for a writer , who uses with freedom the ...
Henry Martyn Taylor. proofs of any theorems , in the proofs of which , in Euclid's text , the theorem of Proposition 4 is quoted . It may of course be fairly objected that it would be more logical for a writer , who uses with freedom the ...
Side x
... theorem from other postulates which have been already assumed . Another new Proposition introduced into the text is Proposition 26 A , " if two triangles have two sides equal to two sides , and the angles opposite to one pair of equal ...
... theorem from other postulates which have been already assumed . Another new Proposition introduced into the text is Proposition 26 A , " if two triangles have two sides equal to two sides , and the angles opposite to one pair of equal ...
Side xi
... theorem . It seems more logical to deduce from Proposition 1 those of the subsequent Propositions which can be ... Theorem " and " Problem . " The student may be informed once for all that the word theorem is used of a geometrical truth ...
... theorem . It seems more logical to deduce from Proposition 1 those of the subsequent Propositions which can be ... Theorem " and " Problem . " The student may be informed once for all that the word theorem is used of a geometrical truth ...
Side xiii
... theorem of Proposition 36 has been altered to make it more closely resemble that of the complementary theorem of Proposition 35 . An additional Proposition has been introduced on ... theorem commonly called Ptolemy's Theorem is not found.
... theorem of Proposition 36 has been altered to make it more closely resemble that of the complementary theorem of Proposition 35 . An additional Proposition has been introduced on ... theorem commonly called Ptolemy's Theorem is not found.
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Vanlige uttrykk og setninger
ABCD ADDITIONAL PROPOSITION AE is equal angle ABC angle ACB angle BAC angular points bisected bisectors centre of similitude chord circle ABC circumscribed circle coincide CONSTRUCTION Coroll cut the circle describe a circle diagonals diameter equal angles equiangular equilateral triangle Euclid EXERCISES figure fixed point given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed circle intersect isosceles triangle Let ABC locus magnitudes meet middle points opposite sides pairs parallel parallelepiped parallelogram perpendicular plane angles polygon PROOF Prop quadrilateral radical axis radius rectangle contained regular polygon required to prove respectively rhombus right angles right-angled triangle shew side BC Similarly solid angle sphere square on AC straight line drawn straight line joining tangent tetrahedron theorem triangle ABC triangles are equal trihedral angle twice the rectangle vertex vertices Wherefore
Populære avsnitt
Side 70 - 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 218 - The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.
Side 279 - 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, together •with the square...
Side 148 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.
Side 137 - 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 372 - 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 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 303 - 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 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Side 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.