The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
From inside the book
Results 1-5 of 12
Page 5
... respectively . A single letter B is sufficient , when there is only one angle at a point ; as the angle E. It is clear that angles are altogether unaffected by the length of the lines , by E the meeting of which they are formed . See ...
... respectively . A single letter B is sufficient , when there is only one angle at a point ; as the angle E. It is clear that angles are altogether unaffected by the length of the lines , by E the meeting of which they are formed . See ...
Page 11
... respectively a question proposed for resolution , and a fact submitted to demonstration . The results of the operation , in the former case , are marked by the letters Q. E. F. ( quod erat faciendum ) , and in the latter , by Q. E. D. ...
... respectively a question proposed for resolution , and a fact submitted to demonstration . The results of the operation , in the former case , are marked by the letters Q. E. F. ( quod erat faciendum ) , and in the latter , by Q. E. D. ...
Page 19
... respectively with E and F , if the base BC does not coincide with the base EF , but lies above or below it , two straight lines would inclose a space , which is impos- sible ( Ax . 10 ) ; .. the base BC coincides with the base EF , and ...
... respectively with E and F , if the base BC does not coincide with the base EF , but lies above or below it , two straight lines would inclose a space , which is impos- sible ( Ax . 10 ) ; .. the base BC coincides with the base EF , and ...
Page 22
... respectively ( Prop . IV . ) But since AB = DF , and AC DE , if the A DEF be B turned over , and applied to the △ DF may coincide with AB , and DE will coincide with B , and the Prop . IV .; .. the C E D F ABC , so that the with AC ...
... respectively ( Prop . IV . ) But since AB = DF , and AC DE , if the A DEF be B turned over , and applied to the △ DF may coincide with AB , and DE will coincide with B , and the Prop . IV .; .. the C E D F ABC , so that the with AC ...
Page 42
... respectively . The following is a practical illus- tration of the property set forth in the Proposition : - Let the △ ABC be moved along the line BE till в coincides with c . B The vertex of the A will now be to the right of A , so ...
... respectively . The following is a practical illus- tration of the property set forth in the Proposition : - Let the △ ABC be moved along the line BE till в coincides with c . B The vertex of the A will now be to the right of A , so ...
Common terms and phrases
ABCD adjacent angle contained base BC bisect CD Prop coincide Const CONST.-In CONST.-Join CONST.-Let DEMONST.-Because DEMONST.-For demonstration diam diameter draw EBCF ENUN ENUN.-If ENUN.-Let ABC ENUN.-To ENUN.-To describe equal sides equilateral Euclid EUCLID'S ELEMENTS exterior four rt given point given straight line interior and opposite interior opposite isosceles join Let ABC line be drawn line drawn meet opposite angles opposite sides parallel parallelogram perpendicular Post PROB produced Proposition proved rectilineal figure rhombus right angles side BC square take any pt THEOR THEOR.-If Theorem trapezium trapezium ABCD vertical Wherefore XXIX XXXI XXXII XXXIV XXXVIII
Popular passages
Page 58 - 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 24 - 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, equal to one another.
Page 34 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 6 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Page 109 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.
Page 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Page 99 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 49 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 104 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Page 6 - 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.