Introduction and books 1,2The University Press, 1908 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 64.
Σελίδα 8
... objection to this theory so far as regards Bryson ; for Alexander distinctly says that Bryson's quadrature did not start from the proper principles of geometry , but from some principles more general . 1 Pappus , VII . p . 638 . Vol ...
... objection to this theory so far as regards Bryson ; for Alexander distinctly says that Bryson's quadrature did not start from the proper principles of geometry , but from some principles more general . 1 Pappus , VII . p . 638 . Vol ...
Σελίδα 23
... objection of any one who should deny our right to assume that there is any space available1 . Of this class are Heron's proofs of I. II , I. 20 , and his note on I. 16. Similarly on I. 48 he supposes the right - angled triangle which is ...
... objection of any one who should deny our right to assume that there is any space available1 . Of this class are Heron's proofs of I. II , I. 20 , and his note on I. 16. Similarly on I. 48 he supposes the right - angled triangle which is ...
Σελίδα 24
... objection which is supposed to require the part of AC equal to AB to be cut off from CA and not from AC . Proclus gives a precisely similar alternative proof of I. 6 to meet a similar supposed objection ; and it may well be that ...
... objection which is supposed to require the part of AC equal to AB to be cut off from CA and not from AC . Proclus gives a precisely similar alternative proof of I. 6 to meet a similar supposed objection ; and it may well be that ...
Σελίδα 28
... objected " even in ancient times " ( iam antiquitus ) to the use by geometers of this postulate . This would not have been an appropriate phrase had Geminus been the writer . I do not think that this difficulty can be got over by ...
... objected " even in ancient times " ( iam antiquitus ) to the use by geometers of this postulate . This would not have been an appropriate phrase had Geminus been the writer . I do not think that this difficulty can be got over by ...
Σελίδα 31
... objections raised by cavillers to particular propositions . The latter class of note he deems necessary because of " sophistical cavils " and the attitude of the people who rejoiced in finding paralogisms and in causing annoyance to ...
... objections raised by cavillers to particular propositions . The latter class of note he deems necessary because of " sophistical cavils " and the attitude of the people who rejoiced in finding paralogisms and in causing annoyance to ...
Συχνά εμφανιζόμενοι όροι και φράσεις
angle ABC angle ACB angle BAC angles equal Apastamba Apollonius Arabic Archimedes Aristotle assumed axiom base BC bisects Book Campanus centre circle circumference coincide commentary Common Notion congruent construction contained definition diameter drawn edition Elements enunciation equal angles equal sides equal to AC Eucl Euclid Euclid's Elements Eudemus Eutocius exterior angle figure Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interpolated isosceles triangle joined lemma length less Let ABC magnitude means meet method observed Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proposition proved Pythagoras Pythagorean Pythagorean theorem quoted rectangle reductio ad absurdum reference remaining angles respectively right angles right-angled triangle says Schol scholia segment semicircle Simplicius Simson square suppose surface Theon Theonine MSS theorem things translation triangle ABC words καὶ τὸ
Δημοφιλή αποσπάσματα
Σελίδα 322 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 204 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 259 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 188 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 204 - In any triangle, the sum of the three angles is equal to two right angles, or 180°.
Σελίδα 162 - A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
Σελίδα 167 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Σελίδα 257 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Σελίδα 176 - Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
Σελίδα 235 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.