The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthR. and A. Foulis, 1762 - 466 sider |
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Side 2
... angles equal to one another , each of the an- gles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII ...
... angles equal to one another , each of the an- gles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII ...
Side 4
... right angle . XXVIII . An obtuse angled triangle , is that which has an obtuse angle . ΧΧΙΧ , An acute angled triangle , is that which has three acute angles ... angles right angles . □□ ΧΧΧΙ . An oblong is that which has all its ...
... right angle . XXVIII . An obtuse angled triangle , is that which has an obtuse angle . ΧΧΙΧ , An acute angled triangle , is that which has three acute angles ... angles right angles . □□ ΧΧΧΙ . An oblong is that which has all its ...
Side 6
... right angles are equal to one another . XII . " If a straight line meets two straight lines , so as to make the two " interior angles on the same side of it taken together less than " two right angles , these straight lines being ...
... right angles are equal to one another . XII . " If a straight line meets two straight lines , so as to make the two " interior angles on the same side of it taken together less than " two right angles , these straight lines being ...
Side 14
... right angles to a given straight line , from a given point in the fame . : Let AB be a given straight line , and C a point given in it ; it is required to draw a straight line from the point C at right angles to AB . F Take any point ...
... right angles to a given straight line , from a given point in the fame . : Let AB be a given straight line , and C a point given in it ; it is required to draw a straight line from the point C at right angles to AB . F Take any point ...
Side 15
... angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ... angles which one straight line makes with ano- ther upon one fide of it , are either two right angles , or are ...
... angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ... angles which one straight line makes with ano- ther upon one fide of it , are either two right angles , or are ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs Let ABC likewife oppoſite parallel parallelepipeds parallelogram perpendicular priſms Propofition proportionals pyramid Q. E. D. PROP rectangle rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AB ſtraight line BC THEOR theſe thoſe tiple triangle ABC vertex wherefore
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Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 163 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Side 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Side 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 54 - 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.
Side 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.