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 sider |
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Resultat 1-5 av 52
Side 39
... ABCD , EBCF be on the same base BC , and between the same parallels AF , BC : the paral- lelogram ABCD shall be equal to the parallelogram EBCF . If the sides AD , DF of the parallelograms ABCD , DBCF , opposite to the base BC , be ...
... ABCD , EBCF be on the same base BC , and between the same parallels AF , BC : the paral- lelogram ABCD shall be equal to the parallelogram EBCF . If the sides AD , DF of the parallelograms ABCD , DBCF , opposite to the base BC , be ...
Side 40
... ABCD , EFGH be parallelograms on equal bases BC , FG , and between the same parallels AH , BG : the parallelogram ABCD shall be equal to the parallelogram EFGH . Join BE , CH . Then , because BC is equal to FG , [ Hyp . and FG to EH ...
... ABCD , EFGH be parallelograms on equal bases BC , FG , and between the same parallels AH , BG : the parallelogram ABCD shall be equal to the parallelogram EFGH . Join BE , CH . Then , because BC is equal to FG , [ Hyp . and FG to EH ...
Side 43
... ABCD and the triangle EBC be on the same base BC , and between the same parallels BC , AE : the parallelogram ABCD shall be double of the triangle EBC . Join AC . Then the triangle ABC is equal to the triangle EBC , because they are on ...
... ABCD and the triangle EBC be on the same base BC , and between the same parallels BC , AE : the parallelogram ABCD shall be double of the triangle EBC . Join AC . Then the triangle ABC is equal to the triangle EBC , because they are on ...
Side 45
... ABCD be a parallelogram , of which the diameter is AC ; and EH , GF parallelograms about AC , that is , through which AC passes ; and BK , KD the other paral- lelograms which make up the whole figure ABCD , and which are therefore ...
... ABCD be a parallelogram , of which the diameter is AC ; and EH , GF parallelograms about AC , that is , through which AC passes ; and BK , KD the other paral- lelograms which make up the whole figure ABCD , and which are therefore ...
Side 47
... ABCD be the given rectilineal figure , and E the given rectilineal angle : it is required to describe a par- allelogram equal to ABCD , and having an angle equal to E. F G B H M Join DB , and describe the parallelogram FH equal to the ...
... ABCD be the given rectilineal figure , and E the given rectilineal angle : it is required to describe a par- allelogram equal to ABCD , and having an angle equal to E. F G B H M Join DB , and describe the parallelogram FH equal to the ...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Issac Todhunter Ingen forhåndsvisning tilgjengelig - 2014 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Side 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.
Side 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.
Side 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.
Side 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 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.
Side 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.