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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 44.
Σελίδα 6
... double of the same thing are equal to one another . 7. Things which are halves of the same thing are equal to one another . 8. Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... double of the same thing are equal to one another . 7. Things which are halves of the same thing are equal to one another . 8. Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Σελίδα 39
... double of the triangle BDC ; B D and they are therefore equal to one another . But if the sides AD , EF , opposite to the of the parallelo- grams ABCD , EBCF be not terminated at DE F [ I. 34 . [ Axiom 6 . base BC D F the same point ...
... double of the triangle BDC ; B D and they are therefore equal to one another . But if the sides AD , EF , opposite to the of the parallelo- grams ABCD , EBCF be not terminated at DE F [ I. 34 . [ Axiom 6 . base BC D F the same point ...
Σελίδα 43
... double of the triangle . Let the parallelogram 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 ...
... double of the triangle . Let the parallelogram 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 ...
Σελίδα 44
... double of the triangle AEC . But the parallelogram FECG is also double of the triangle AEC , because they are on the same base EC , and between the same parallels EC , AG . [ I. 41 . [ Axiom 6 . Therefore the parallelogram FECG is equal ...
... double of the triangle AEC . But the parallelogram FECG is also double of the triangle AEC , because they are on the same base EC , and between the same parallels EC , AG . [ I. 41 . [ Axiom 6 . Therefore the parallelogram FECG is equal ...
Σελίδα 50
... to each ; [ Definition 30 . and the angle DBA is equal to the angle FBC ; therefore the triangle ABD is equal to the triangle FBC . [ I. 4 . Now the parallelogram BL is double of the triangle ABD 50 EUCLID'S ELEMENTS .
... to each ; [ Definition 30 . and the angle DBA is equal to the angle FBC ; therefore the triangle ABD is equal to the triangle FBC . [ I. 4 . Now the parallelogram BL is double of the triangle ABD 50 EUCLID'S ELEMENTS .
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Issac Todhunter Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2014 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 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.
Σελίδα 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.