A Text-book of Euclid's Elements for the Use of Schools, Βιβλίο 1Macmillan, 1904 - 456 σελίδες |
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Αποτελέσματα 1 - 5 από τα 15.
Σελίδα 23
... Нур . therefore the angle BDC is equal to the angle BCD : 1.5 . but it has been shewn to be greater ; which is impossible . The case in which the vertex of one triangle is on a side of the other needs no demonstration . Therefore AC ...
... Нур . therefore the angle BDC is equal to the angle BCD : 1.5 . but it has been shewn to be greater ; which is impossible . The case in which the vertex of one triangle is on a side of the other needs no demonstration . Therefore AC ...
Σελίδα 41
... Нур . for then the angle ABC would be less than the angle ACB ; I. 18 . but it is not . Hyp . That is , AC is neither equal to , nor less than AB . Therefore AC is greater than AB . Q.E.D. NOTE . The mode of demonstration used in this ...
... Нур . for then the angle ABC would be less than the angle ACB ; I. 18 . but it is not . Hyp . That is , AC is neither equal to , nor less than AB . Therefore AC is greater than AB . Q.E.D. NOTE . The mode of demonstration used in this ...
Σελίδα 99
... Нур . I. 14 . Нур . I. 5 . Proved . I. 26 . Q.E. D. I. 47 . I. 47 . And of these , the sq . on AB the sq . on DE , since AB = DE ; on BC the sq . on EF ; .. the sq . .. BC = EF . Ax . 3 . Hence the three sides of the ABC are ...
... Нур . I. 14 . Нур . I. 5 . Proved . I. 26 . Q.E. D. I. 47 . I. 47 . And of these , the sq . on AB the sq . on DE , since AB = DE ; on BC the sq . on EF ; .. the sq . .. BC = EF . Ax . 3 . Hence the three sides of the ABC are ...
Σελίδα 100
... Нур . 1. 5 . I. 13 . Q.E.D. Three cases of this theorem deserve special It has been proved that if the angles ACB , DFE are not supple- mentary they are equal : Hence , in addition to the hypothesis of this theorem 100 . EUCLID'S ELEMENTS .
... Нур . 1. 5 . I. 13 . Q.E.D. Three cases of this theorem deserve special It has been proved that if the angles ACB , DFE are not supple- mentary they are equal : Hence , in addition to the hypothesis of this theorem 100 . EUCLID'S ELEMENTS .
Σελίδα 104
... Нур . X I. 26 . I. 34 . Q. E.D. But ZXCY is a parm by construction ; .. ZX = YC . Hence AYYC ; that is , AC is bisected at Y. 2. The straight line which joins the middle points of two sides of a triangle , is parallel to the third side ...
... Нур . X I. 26 . I. 34 . Q. E.D. But ZXCY is a parm by construction ; .. ZX = YC . Hence AYYC ; that is , AC is bisected at Y. 2. The straight line which joins the middle points of two sides of a triangle , is parallel to the third side ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 340 - 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.
Σελίδα 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Σελίδα 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Σελίδα 162 - 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...
Σελίδα 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 18 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.