Introduction and books 1,2 |
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Page 403
In obtuse - angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides containing the ootuse angle by twice the rectangle contained by one of the sides about the obtuse angle , namely ...
In obtuse - angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides containing the ootuse angle by twice the rectangle contained by one of the sides about the obtuse angle , namely ...
Page 404
Let ABC be an obtuse - angled triangle having the angle BAC obtuse , and let BD be drawn from the point 3 perpendicular to CA produced ; I say that the square on BC is greater than the squares on BA , AC by twice the rectangle contained ...
Let ABC be an obtuse - angled triangle having the angle BAC obtuse , and let BD be drawn from the point 3 perpendicular to CA produced ; I say that the square on BC is greater than the squares on BA , AC by twice the rectangle contained ...
Page 405
But the rectangles AR , AQ are equal , and they are respectively the rectangle contained by BA , AN and the ... on one of the sides is greater than the squares on the other two sides , the angle contained by the latter is obtuse .
But the rectangles AR , AQ are equal , and they are respectively the rectangle contained by BA , AN and the ... on one of the sides is greater than the squares on the other two sides , the angle contained by the latter is obtuse .
Page 406
Therefore the angle BAC is greater than the angle DAC ; that is , the angle BAC is obtuse . ... the squares on the sides containing the acute angle by twice the rectangle contained by one of the sides about the acute angle , namely that ...
Therefore the angle BAC is greater than the angle DAC ; that is , the angle BAC is obtuse . ... the squares on the sides containing the acute angle by twice the rectangle contained by one of the sides about the acute angle , namely that ...
Page 407
is curious that it speaks of the square on the side subtending the acute angle ; and again the setting - out begins “ let ABC be an acute - angled triangle having the ... sides containing the acute angle by twice the rectangle , etc.
is curious that it speaks of the square on the side subtending the acute angle ; and again the setting - out begins “ let ABC be an acute - angled triangle having the ... sides containing the acute angle by twice the rectangle , etc.
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Interestingly, this scan is missing pages 250 and 251, which covers Proposition 5 of Book 1 (the "pons asinorum").
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according added addition alternative Apollonius appears Aristotle assumed axiom base Book called centre circle coincide commentary Common Notion conclusion congruent construction contained converse corresponding definition described direction distance draw drawn edition Elements enunciation equal Euclid existence explain expression extremity fact figure follows geometry given gives greater Greek hand Heiberg Heron hypothesis impossible included joined latter lemma length less magnitude means meet mentioned method namely necessary objection observed opposite original Pappus parallel parallelogram particular passage perpendicular plane position possible postulate principles problem Proclus produced proof proposition proved quoted reason rectangle reference regards remaining remarks respectively right angles says scholia seems segment sense sides similar solid square straight line suppose surface taken takes term theorem things translation triangle true whole
Popular passages
Page 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.
Page 204 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 259 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
Page 204 - In any triangle, the sum of the three angles is equal to two right angles, or 180°.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Bibliographic information
| Title | Introduction and books 1,2 Volume 1 of The Thirteen Books of Euclid's Elements, Sir Thomas Little Heath |
| Author | Euclid |
| Publisher | The University Press, 1908 |
| Export Citation | BiBTeX EndNote RefMan |