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 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 43.
Σελίδα 11
... 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.
... 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 12
... equiangular triangle is also PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there can- not be two triangles having their sides which are terminated at one extremity of the base equal to one another , and ...
... equiangular triangle is also PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there can- not be two triangles having their sides which are terminated at one extremity of the base equal to one another , and ...
Σελίδα 115
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle : it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw the straight line GAH touching the circle at the ...
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle : it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw the straight line GAH touching the circle at the ...
Σελίδα 116
... equiangular to the triangle DEF . Produce EF both ways to the points G , H ; take Ŕ the centre of the circle ABC ; [ III . 1 . from K draw any radius KB ; at the point K , in the straight line KB , make the angle BKÁ equal to the angle ...
... equiangular to the triangle DEF . Produce EF both ways to the points G , H ; take Ŕ the centre of the circle ABC ; [ III . 1 . from K draw any radius KB ; at the point K , in the straight line KB , make the angle BKÁ equal to the angle ...
Σελίδα 117
... equiangular to the tri- angle DEF , and it is described about the circle ABC . Q.E.F , PROPOSITION 4. PROBLEM . To inscribe a circle in a given triangle . Let ABC be the given triangle : it is required to inscribe a circle in the ...
... equiangular to the tri- angle DEF , and it is described about the circle ABC . Q.E.F , PROPOSITION 4. PROBLEM . To inscribe a circle in a given triangle . Let ABC be the given triangle : it is required to inscribe a circle in the ...
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.