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 3
... diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the circumference which it cuts off . 20. Rectilineal figures are those which are contained by ...
... diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the circumference which it cuts off . 20. Rectilineal figures are those which are contained by ...
Seite 37
... diameter bisects the par- allelogram , that is , divides it into two equal parts . Note . A parallelogram is a four - sided figure of which the opposite sides are parallel ; and a diameter is the straight line joining two of its ...
... diameter bisects the par- allelogram , that is , divides it into two equal parts . Note . A parallelogram is a four - sided figure of which the opposite sides are parallel ; and a diameter is the straight line joining two of its ...
Seite 38
... diameter ; the opposite sides and angles of the figure shall be equal to one another , and the diameter BC shall bi- sect it . Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to one an- other ...
... diameter ; the opposite sides and angles of the figure shall be equal to one another , and the diameter BC shall bi- sect it . Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to one an- other ...
Seite 41
... diameter AB bisects the parallelogram ; [ I. 34 . and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects the parallelogram . [ I. 34 . But the halves of equal things are equal . [ Axiom 7 . Therefore ...
... diameter AB bisects the parallelogram ; [ I. 34 . and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects the parallelogram . [ I. 34 . But the halves of equal things are equal . [ Axiom 7 . Therefore ...
Seite 43
... diameter AC bisects the parallelogram . [ I. 34 . Therefore the parallelogram ABCD is also double of the triangle EBC . Wherefore , if a parallelogram & c . Q.E.D. PROPOSITION 42. PROBLEM . To describe a parallelogram that shall BOOK I ...
... diameter AC bisects the parallelogram . [ I. 34 . Therefore the parallelogram ABCD is also double of the triangle EBC . Wherefore , if a parallelogram & c . Q.E.D. PROPOSITION 42. PROBLEM . To describe a parallelogram that shall BOOK I ...
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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.