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 twelfth |
From inside the book
Page 3
... Some of Euclid's Demonstrations are Restored. Also, to this Second ... one line , which is called the circumference , and is fuch that all straight lines drawn from a cer- tain point within the figure to the circumference , are equal to one ...
... Some of Euclid's Demonstrations are Restored. Also, to this Second ... one line , which is called the circumference , and is fuch that all straight lines drawn from a cer- tain point within the figure to the circumference , are equal to one ...
Page 60
... figure con- tained by a straight line and the cir- cumference it cuts off . VII . " The angle of a segment is that which is contained by the straight " line and the circumference ... lines drawn from any point in the circumference of the ...
... figure con- tained by a straight line and the cir- cumference it cuts off . VII . " The angle of a segment is that which is contained by the straight " line and the circumference ... lines drawn from any point in the circumference of the ...
Page 86
... one angle of a triangle be equal to the other two , it is a right angle ... point of II . I. angles made by this line with the line touching the circle ... drawn cutting the circle . the angles which BD makes with the touching line EF ...
... one angle of a triangle be equal to the other two , it is a right angle ... point of II . I. angles made by this line with the line touching the circle ... drawn cutting the circle . the angles which BD makes with the touching line EF ...
Page 95
... points of the figure about which it is described . VII . Aftraight line is faid to be placed in a circle , when the extremities of it are in the circumference of the circle . PROP . I. PROB . a a given circle to place a ftraight line , ...
... points of the figure about which it is described . VII . Aftraight line is faid to be placed in a circle , when the extremities of it are in the circumference of the circle . PROP . I. PROB . a a given circle to place a ftraight line , ...
Page 281
... point A. and the fuperficies of this folid polyhedron does not meet the ... equal to AK , and that the squares of AZ , ZB , are equal to the square of ... lines drawn from the point Z to the points O , S are equal to BZ or ZK . therefore ...
... point A. and the fuperficies of this folid polyhedron does not meet the ... equal to AK , and that the squares of AZ , ZB , are equal to the square of ... lines drawn from the point Z to the points O , S are equal to BZ or ZK . therefore ...
Other editions - View all
Common terms and phrases
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated drawn equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fame reaſon fecond fegment fhall fhewn fides fimilar firft firſt folid angle fome fore fquare of BC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs Let ABC likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular polygon prifms Propofition proportionals pyramid Q. E. D. PROP reafon rectangle rectangle contained rectilineal figure right angles ſhall ſphere ſquare ſtraight line AB thefe THEOR theſe thro tiple triangle ABC wherefore
Popular passages
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.
Page 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 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.
Page 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.
Page 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.