The Elements of Euclid for the Use of Schools and Colleges: With Notes, an Appendix, and Exercises. comprising the first six books and portions of the eleventh and twelfth booksMacmillan and Company, 1880 - 400 Seiten |
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Seite 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 ...
Seite 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.
Seite 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 ...
Seite 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 ...
Seite 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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Häufige Begriffe und Wortgruppen
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC 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
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Seite 225 - 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.
Seite 284 - 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 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Seite 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Seite 10 - 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.
Seite 353 - 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.
Seite 67 - ... subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle ACB; and from the point A, let AD be drawn perpendicular to BC produced.
Seite 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite xv - PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given Jinite straight line. Let AB be the given straight line. It is required to describe an equilateral triangle upon AB, From the centre A, at the distance AB, describe the circle BCD ; (post.
Seite 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.