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 93.
Σελίδα 7
... , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
... , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
Σελίδα 8
... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be ...
... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight lines to cut off a part equal to the less Let AB and C be ...
Σελίδα 11
... angle GCB , which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
... angle GCB , which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
Σελίδα 14
... Wherefore , if two triangles & c . Q.E.D. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle it is required 14 EUCLID'S ELEMENTS .
... Wherefore , if two triangles & c . Q.E.D. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle it is required 14 EUCLID'S ELEMENTS .
Σελίδα 15
... Wherefore the given rectilineal angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION 10. PROBLEM . To bisect a given finite straight line , that is to divide it into two equal parts . Let AB be the given straight line : it ...
... Wherefore the given rectilineal angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION 10. PROBLEM . To bisect a given finite straight line , that is to divide it into two equal parts . Let AB be the given straight line : it ...
Άλλες εκδόσεις - Προβολή όλων
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.