The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Σελίδα 13
... AC , AF , and BC , BF . A more general proposition than the following will be seen under Prop . III . See also Prop . XXII . C E This Problem is practically applied in Fortification . C B PROP . A. PROB . GEN . ENUN . - 13.
... AC , AF , and BC , BF . A more general proposition than the following will be seen under Prop . III . See also Prop . XXII . C E This Problem is practically applied in Fortification . C B PROP . A. PROB . GEN . ENUN . - 13.
Σελίδα 18
... applied to the DEF , so that the pt . A may be on D , and the st . line AB upon DE ; the pt . B shall coincide with the pt . E , because AB = DE . ( Hyp . ) 2. Also , AB coinciding with DE , AC shall fall upon DF , because the BAC EDF ...
... applied to the DEF , so that the pt . A may be on D , and the st . line AB upon DE ; the pt . B shall coincide with the pt . E , because AB = DE . ( Hyp . ) 2. Also , AB coinciding with DE , AC shall fall upon DF , because the BAC EDF ...
Σελίδα 22
... 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 , the F with c , as in B and c are each = each other . - Q . E. D. E = E , and ... they In forming ...
... 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 , the F with c , as in B and c are each = each other . - Q . E. D. E = E , and ... they In forming ...
Σελίδα 27
... applied to the D G cide with F , be- cause BC = EF . B E F ( Hyp . ) 2. Now BC coinciding with EF , AB , AC shall also coincide with DE , DF . For if AB , AC , do not coincide with DE , DF , but take another direction , as , for ...
... applied to the D G cide with F , be- cause BC = EF . B E F ( Hyp . ) 2. Now BC coinciding with EF , AB , AC shall also coincide with DE , DF . For if AB , AC , do not coincide with DE , DF , but take another direction , as , for ...
Σελίδα 29
... applied to the a DEF , so that the pt . в be on E , and the st . line BC on EF , the pt . c shall coin- cide with F , be- cause BC = EF . ( Hyp . ) A A B F 2. Now BC coinciding with EF , AB , AC shall also coincide with DE , DF . For if ...
... applied to the a DEF , so that the pt . в be on E , and the st . line BC on EF , the pt . c shall coin- cide with F , be- cause BC = EF . ( Hyp . ) A A B F 2. Now BC coinciding with EF , AB , AC shall also coincide with DE , DF . For if ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.