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 86.
Σελίδα xvi
... hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the demonstration . Thus I. 5 indicates ...
... hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the demonstration . Thus I. 5 indicates ...
Σελίδα 10
... Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the base BC will coincide with the base EF ; because ...
... Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the base BC will coincide with the base EF ; because ...
Σελίδα 11
... 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 the base FC is equal to the base GB , and the triangle ...
... 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 the base FC is equal to the base GB , and the triangle ...
Σελίδα 13
... Hypothesis . b [ I. 5 . α But the angle 4D is greater than the angle BCD , [ Ax . 9 . therefore the angle ABC is also greater than the angle BOD ; c + much more then is the angle greater than the angle BOD . Again , because BC is equal ...
... Hypothesis . b [ I. 5 . α But the angle 4D is greater than the angle BCD , [ Ax . 9 . therefore the angle ABC is also greater than the angle BOD ; c + much more then is the angle greater than the angle BOD . Again , because BC is equal ...
Σελίδα 16
... draw BE at right angles to AB . E B the angle CBE is equal to the angle EBA . [ Hypothesis . [ Definition 10 . Then , because ABC is a straight line , Also , because ABD is a straight line , the 16 EUCLID'S ELEMENTS .
... draw BE at right angles to AB . E B the angle CBE is equal to the angle EBA . [ Hypothesis . [ Definition 10 . Then , because ABC is a straight line , Also , because ABD is a straight line , the 16 EUCLID'S ELEMENTS .
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.