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 82.
Σελίδα 11
... join FC , GB . Because AF'is equal to AG , [ Constr . [ Hypothesis . and AB to AC , the two sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle A common to the two triangles AFC , AGB ; therefore ...
... join FC , GB . Because AF'is equal to AG , [ Constr . [ Hypothesis . and AB to AC , the two sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle A common to the two triangles AFC , AGB ; therefore ...
Σελίδα 15
... join DE , and on DE , on the side remote from A , describe the equi- lateral triangle DEF . [ 1. 1 . B Join AF . The straight line AF shall bisect the angle BAC . Because AD is equal to AE , [ Construction . and AF is common to the two ...
... join DE , and on DE , on the side remote from A , describe the equi- lateral triangle DEF . [ 1. 1 . B Join AF . The straight line AF shall bisect the angle BAC . Because AD is equal to AE , [ Construction . and AF is common to the two ...
Σελίδα 16
... join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , [ Construction . and CF is common to the two triangles DCF , ECF ; the two sides DC ...
... join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , [ Construction . and CF is common to the two triangles DCF , ECF ; the two sides DC ...
Σελίδα 17
... join CH . CF and CG . The straight line CH drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal to HG , [ Construction . and HC is common to the two triangles FHC , GHC ...
... join CH . CF and CG . The straight line CH drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal to HG , [ Construction . and HC is common to the two triangles FHC , GHC ...
Σελίδα 20
... join BE and produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is equal to ...
... join BE and produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is equal to ...
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.