Introduction and books 1,2The University Press, 1908 |
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Σελίδα 25
... converse , viz . that all angles equal to a right angle are right , is not true , since the angle included between the arcs of two semicircles which are equal , and have their diameters at right angles and terminating at one point , is ...
... converse , viz . that all angles equal to a right angle are right , is not true , since the angle included between the arcs of two semicircles which are equal , and have their diameters at right angles and terminating at one point , is ...
Σελίδα 26
... converse ( that a figure with its interior angles together equal to two right angles is a triangle ) is not true unless we confine ourselves to rectilineal figures . This statement is supported by reference to a figure formed by four ...
... converse ( that a figure with its interior angles together equal to two right angles is a triangle ) is not true unless we confine ourselves to rectilineal figures . This statement is supported by reference to a figure formed by four ...
Σελίδα 33
... converse of I. 32 is proved " , the proposition namely that a rectilineal figure which has all its interior angles together equal to two right angles is a triangle . " " It is not safe to attribute a passage to Proclus himself because ...
... converse of I. 32 is proved " , the proposition namely that a rectilineal figure which has all its interior angles together equal to two right angles is a triangle . " " It is not safe to attribute a passage to Proclus himself because ...
Σελίδα 42
... converse of I. 172 . Of the authors to whom Proclus was indebted in a less degree the most important is Apollonius of Perga . Two passages allude to his Conics , one to a work on irrationals , and two to a treatise On the cochlias ...
... converse of I. 172 . Of the authors to whom Proclus was indebted in a less degree the most important is Apollonius of Perga . Two passages allude to his Conics , one to a work on irrationals , and two to a treatise On the cochlias ...
Σελίδα 158
... converse is of course not true . Alternative definitions . The alternative definition alluded to by Proclus , μέγεθος ἐφ ' εν διαστατόν magnitude in one dimension " or , better perhaps , " magnitude extended one way " ( since diaoraσis ...
... converse is of course not true . Alternative definitions . The alternative definition alluded to by Proclus , μέγεθος ἐφ ' εν διαστατόν magnitude in one dimension " or , better perhaps , " magnitude extended one way " ( since diaoraσis ...
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.