Introduction and books 1,2The University Press, 1908 |
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Σελίδα 13
... prove ) that the angles at the base of isosceles triangles are equal is a matter of theoretic argument , and it is with ... proved , that certain points lie on straight lines given in position , with the class indicated by II . above ...
... prove ) that the angles at the base of isosceles triangles are equal is a matter of theoretic argument , and it is with ... proved , that certain points lie on straight lines given in position , with the class indicated by II . above ...
Σελίδα 21
... proved by Heron in his Catoptrica , coupled with the facts that in that work Heron mentions Menelaus of Alexandria ( about 100 A.D. ) and that Plutarch died at a great age in 120 A.D. Attempts have however been made in two recent tracts ...
... proved by Heron in his Catoptrica , coupled with the facts that in that work Heron mentions Menelaus of Alexandria ( about 100 A.D. ) and that Plutarch died at a great age in 120 A.D. Attempts have however been made in two recent tracts ...
Σελίδα 33
... proved by Euclid , selecting the more subtle of the comments made on them by the ancient writers , and cutting down their interminable diffuse- ness ... " : not a word about anything of his own . At the same time , he seems to imply ...
... proved by Euclid , selecting the more subtle of the comments made on them by the ancient writers , and cutting down their interminable diffuse- ness ... " : not a word about anything of his own . At the same time , he seems to imply ...
Σελίδα 40
... prove axioms , as Apollonius tried to prove Axiom 1 , and the equal incorrectness of assuming what really requires proof ... proved that the only " uniform lines ” their pneumatic devices ( @ avμaroroký ) , as regards which Proclus ...
... prove axioms , as Apollonius tried to prove Axiom 1 , and the equal incorrectness of assuming what really requires proof ... proved that the only " uniform lines ” their pneumatic devices ( @ avμaroroký ) , as regards which Proclus ...
Σελίδα 59
... proving what it was required to prove in it . But I will show how it is to be proved if the contact be external . " This additional proposition of Heron's is by way of adding another case , which brings us to that class of interpolation ...
... proving what it was required to prove in it . But I will show how it is to be proved if the contact be external . " This additional proposition of Heron's is by way of adding another case , which brings us to that class of interpolation ...
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.