The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1867 - 400 sider |
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Side ix
... difference in the size of the pages . It will be perceived then , that in the present edition each distinct assertion in the argument begins a new line ; and at the ends of the lines are placed the necessary refer- ences to the ...
... difference in the size of the pages . It will be perceived then , that in the present edition each distinct assertion in the argument begins a new line ; and at the ends of the lines are placed the necessary refer- ences to the ...
Side 57
... difference of the squares on two unequal straight lines AC , CD , is equal to the rectangle contained by their sum and difference . PROPOSITION 6. THEOREM . If a straight line be bisected BOOK II . 5 . 57.
... difference of the squares on two unequal straight lines AC , CD , is equal to the rectangle contained by their sum and difference . PROPOSITION 6. THEOREM . If a straight line be bisected BOOK II . 5 . 57.
Side 133
... difference , the arc BC , contains two of the same parts . Bisect the arc BC at E ; [ III . 30 . therefore each of the arcs BE , EC is the fifteenth part of the whole circumference ABCDF . Therefore if the straight lines BE , EC be ...
... difference , the arc BC , contains two of the same parts . Bisect the arc BC at E ; [ III . 30 . therefore each of the arcs BE , EC is the fifteenth part of the whole circumference ABCDF . Therefore if the straight lines BE , EC be ...
Side 269
... difference of two straight lines is equal to the difference of the squares described on those straight lines ; or thus , the rectangle contained by two straight lines together with the square described on half their difference , is ...
... difference of two straight lines is equal to the difference of the squares described on those straight lines ; or thus , the rectangle contained by two straight lines together with the square described on half their difference , is ...
Side 275
... B and C double of D ; then in the first part it is assumed that the sum of A and C is double of the sum of B and D , and in the second part it is as- sumed that the difference of A and C is double 18-2 EUCLID'S ELEMENTS . 275.
... B and C double of D ; then in the first part it is assumed that the sum of A and C is double of the sum of B and D , and in the second part it is as- sumed that the difference of A and C is double 18-2 EUCLID'S ELEMENTS . 275.
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Vanlige uttrykk og setninger
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Populære avsnitt
Side 286 - 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 30 - 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. either the sides adjacent to the equal...
Side 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Side 37 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Side 12 - 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.
Side 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Side 104 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.