Introduction and books 1,2The University Press, 1908 |
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Σελίδα 5
... added to the doctrine of the five regular solids . ) To the thirteen books were added two more books , the work of others ( though some attribute these also to Euclid ) which contain several things not mentioned by Apollonius ...
... added to the doctrine of the five regular solids . ) To the thirteen books were added two more books , the work of others ( though some attribute these also to Euclid ) which contain several things not mentioned by Apollonius ...
Σελίδα 6
... added to the doctrine of the five solids , seems to have arisen , through a like confusion , out of a later passage ' in Hypsicles ' Book XIV .: " And this is expounded by Aristaeus in the book entitled ' Comparison of the five figures ...
... added to the doctrine of the five solids , seems to have arisen , through a like confusion , out of a later passage ' in Hypsicles ' Book XIV .: " And this is expounded by Aristaeus in the book entitled ' Comparison of the five figures ...
Σελίδα 10
... added nothing to what was written originally by Euclid , except that some before my time have shown their want of taste by adding to a few ( of the propositions ) second proofs , each ( proposition ) admitting of a definite number of ...
... added nothing to what was written originally by Euclid , except that some before my time have shown their want of taste by adding to a few ( of the propositions ) second proofs , each ( proposition ) admitting of a definite number of ...
Σελίδα 16
... added four more and gave us eight books of Conics " It is probable that Euclid's work was lost even by Pappus ' time ... adding in three cases that they are proved in the " elements of conics " or in " the conics , " which expressions ...
... added four more and gave us eight books of Conics " It is probable that Euclid's work was lost even by Pappus ' time ... adding in three cases that they are proved in the " elements of conics " or in " the conics , " which expressions ...
Σελίδα 25
... added to equals and equals added to unequals " ; these , says Proclus , follow from the Euclidean axioms , while others given by Pappus are involved by the definitions , namely those which assert that " all parts of the plane and of the ...
... added to equals and equals added to unequals " ; these , says Proclus , follow from the Euclidean axioms , while others given by Pappus are involved by the definitions , namely those which assert that " all parts of the plane and of the ...
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.