Introduction and books 1,2The University Press, 1908 |
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Αποτελέσματα 1 - 5 από τα 95.
Σελίδα v
... true that in the interval much valuable work has been done on the continent in the investigation of the first principles , including the formulation and classification of axioms or postulates which are necessary to make good the ...
... true that in the interval much valuable work has been done on the continent in the investigation of the first principles , including the formulation and classification of axioms or postulates which are necessary to make good the ...
Σελίδα xiii
... true that in the interval much valuable work has been done on the continent in the investigation of the first principles , including the formulation and classification of axioms or postulates which are necessary to make good the ...
... true that in the interval much valuable work has been done on the continent in the investigation of the first principles , including the formulation and classification of axioms or postulates which are necessary to make good the ...
Σελίδα 2
... true that Euclid's Elements end with the construction of the five regular solids ; but the planimetrical portion has no direct relation to them , and the arithmetical no relation at all ; the propositions about them are merely the ...
... true that Euclid's Elements end with the construction of the five regular solids ; but the planimetrical portion has no direct relation to them , and the arithmetical no relation at all ; the propositions about them are merely the ...
Σελίδα 3
... true . According to Stobaeus , " some one who had begun to read geometry with Euclid when he had learnt the first theorem , asked Euclid , ' But what shall I get by learning these things ? ' Euclid called his slave and said ' Give him ...
... true . According to Stobaeus , " some one who had begun to read geometry with Euclid when he had learnt the first theorem , asked Euclid , ' But what shall I get by learning these things ? ' Euclid called his slave and said ' Give him ...
Σελίδα 7
... true side by side with the false , and combining the refutation of error with practical illustration . This book then is by way of cathartic and exercise , while the Elements contain the irrefragable and complete guide to the actual ...
... true side by side with the false , and combining the refutation of error with practical illustration . This book then is by way of cathartic and exercise , while the Elements contain the irrefragable and complete guide to the actual ...
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.