Introduction and books 1,2The University Press, 1908 |
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Σελίδα 10
... enunciations can be formed like those of either theorems or problems ] , the result being that , of the great number of geometers , some regarded them as of the class of theorems , and others of pro- blems , looking only to the form of ...
... enunciations can be formed like those of either theorems or problems ] , the result being that , of the great number of geometers , some regarded them as of the class of theorems , and others of pro- blems , looking only to the form of ...
Σελίδα 11
... enunciation is by no means easy in these porisms , because Euclid himself has not in fact given many of each species , but chosen , for examples , one or a few out of a great multitude . But at the beginning of the first book he has ...
... enunciation is by no means easy in these porisms , because Euclid himself has not in fact given many of each species , but chosen , for examples , one or a few out of a great multitude . But at the beginning of the first book he has ...
Σελίδα 12
Euclid. " This has only been enunciated of four straight lines , of which not more than two pass through the same point , but it is not known ( to most people ) that it is true of any assigned number of straight lines if enunciated thus ...
Euclid. " This has only been enunciated of four straight lines , of which not more than two pass through the same point , but it is not known ( to most people ) that it is true of any assigned number of straight lines if enunciated thus ...
Σελίδα 13
... enunciation given by Pappus as comprehending ten of Euclid's propositions may not reproduce the form of Euclid's enunciations ; but , comparing the result to be proved , that certain points lie on straight lines given in position , with ...
... enunciation given by Pappus as comprehending ten of Euclid's propositions may not reproduce the form of Euclid's enunciations ; but , comparing the result to be proved , that certain points lie on straight lines given in position , with ...
Σελίδα 14
... enunciation something is taken into the hypothesis which was not in the hypothesis of the enunciation of the porism , viz . " that the ratio of the straight lines is the same . ' I confess this does not seem to me satisfactory : for ...
... enunciation something is taken into the hypothesis which was not in the hypothesis of the enunciation of the porism , viz . " that the ratio of the straight lines is the same . ' I confess this does not seem to me satisfactory : for ...
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.