Introduction and books 1,2The University Press, 1908 |
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Σελίδα 2
... regards the learner , and would say as regards ( 1 ) that " the whole of the geometer's argument is concerned with the cosmic figures . " This latter statement is obviously incorrect . It is true that Euclid's Elements end with the ...
... regards the learner , and would say as regards ( 1 ) that " the whole of the geometer's argument is concerned with the cosmic figures . " This latter statement is obviously incorrect . It is true that Euclid's Elements end with the ...
Σελίδα 7
... regard to them , reference should be made to the standard histories of mathematics ' . I will take first the works which are mentioned by Greek authors . 1. The Pseudaria . I mention this first because Proclus refers to it in the ...
... regard to them , reference should be made to the standard histories of mathematics ' . I will take first the works which are mentioned by Greek authors . 1. The Pseudaria . I mention this first because Proclus refers to it in the ...
Σελίδα 8
... 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 . VI . in the Teubner edition of ...
... 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 . VI . in the Teubner edition of ...
Σελίδα 15
... regard to the conditions to which the lines in the figure may be subject would suggest that other loci dealt with were cones regarded as containing all points on particular elliptical parallel sections of the cones " . ( 2 ) In the ...
... regard to the conditions to which the lines in the figure may be subject would suggest that other loci dealt with were cones regarded as containing all points on particular elliptical parallel sections of the cones " . ( 2 ) In the ...
Σελίδα 16
... regards the contents of Euclid's Conics , the most important source of our information is Archimedes , who frequently refers to propositions in conics as well known and not needing proof , adding in three cases that they are proved in ...
... regards the contents of Euclid's Conics , the most important source of our information is Archimedes , who frequently refers to propositions in conics as well known and not needing proof , adding in three cases that they are proved in ...
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.