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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Resultat 1-5 av 68
Side 5
... parallelogram . The words square and rhombus are used in the sense defined by Euclid ; and the word rectangle is used instead of the word oblong . Some writers propose to restrict the word trapezium to a quadrilateral which has two of ...
... parallelogram . The words square and rhombus are used in the sense defined by Euclid ; and the word rectangle is used instead of the word oblong . Some writers propose to restrict the word trapezium to a quadrilateral which has two of ...
Side 37
... parallelogram are equal to one another , and the 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 ...
... parallelogram are equal to one another , and the 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 ...
Side 38
... parallelogram are equal to one another . Also the diameter bisects the parallelogram . For AB being equal to CD , and BC common , the two sides AB , BC are equal to the two sides DC , CB each to each ; and the angle ABC has been shewn ...
... parallelogram are equal to one another . Also the diameter bisects the parallelogram . For AB being equal to CD , and BC common , the two sides AB , BC are equal to the two sides DC , CB each to each ; and the angle ABC has been shewn ...
Side 39
... parallelogram EBCF . If the sides AD , DF of the parallelograms ABCD , DBCF , opposite to the base BC , be terminated at the same point D , it is plain that each of the parallelograms is double of the triangle BDC ; A B and they are ...
... parallelogram EBCF . If the sides AD , DF of the parallelograms ABCD , DBCF , opposite to the base BC , be terminated at the same point D , it is plain that each of the parallelograms is double of the triangle BDC ; A B and they are ...
Side 40
... parallelogram ABCD shall be equal to the parallelogram EFGH . Join BE , CH . Then , because BC is equal to FG , [ Hyp . A E H and FG to EH , [ I. 34 . BC is equal to EH ; [ Axiom 1 . B and they are parallels , [ Hypothesis . and joined ...
... parallelogram ABCD shall be equal to the parallelogram EFGH . Join BE , CH . Then , because BC is equal to FG , [ Hyp . A E H and FG to EH , [ I. 34 . BC is equal to EH ; [ Axiom 1 . B and they are parallels , [ Hypothesis . and joined ...
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The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1884 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1883 |
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.