The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope |
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Αποτελέσματα 1 - 5 από τα 8.
Σελίδα 13
... longer than either of the two equal sides AC , AF , and BC , BF . A more general
proposition than the following will be seen under Prop . III . See also Prop . XXII .
This Problem is practically applied in Fortification . E PROP . A . PROB . Gen .
... longer than either of the two equal sides AC , AF , and BC , BF . A more general
proposition than the following will be seen under Prop . III . See also Prop . XXII .
This Problem is practically applied in Fortification . E PROP . A . PROB . Gen .
Σελίδα 18
... and AC = DF , and BL also the < BAC = Z EDF ; then the base BC shall = base
EF ; and the area of the A ABC shall = area of a DEF ; also the ABC shall = < DEF
; another 2 ACB shall = ZDFE . DEMONST . - 1 . For if the A ABC be applied to ...
... and AC = DF , and BL also the < BAC = Z EDF ; then the base BC shall = base
EF ; and the area of the A ABC shall = area of a DEF ; also the ABC shall = < DEF
; another 2 ACB shall = ZDFE . DEMONST . - 1 . For if the A ABC be applied to ...
Σελίδα 22
But since AB = df , and AC = DE , if the A DEF be Bo turned over , and applied to
the A ABC , so that the DF may coincide with AB , and de with AC , the LF will
coincide with / B , and the / E with c , as in Prop . IV . ; . . . the 48 B and c are each
...
But since AB = df , and AC = DE , if the A DEF be Bo turned over , and applied to
the A ABC , so that the DF may coincide with AB , and de with AC , the LF will
coincide with / B , and the / E with c , as in Prop . IV . ; . . . the 48 B and c are each
...
Σελίδα 27
For if the A ABC be applied to the A DEF , so that the G pt . B be on E , and the st .
line BC on EF , the pt . c shall coincide with F , because BC = EF . ( Hyp . ) 2 .
Now bc coinciding with EF , AB , AC shall also coincide with DE , DF . For if AB ,
AC ...
For if the A ABC be applied to the A DEF , so that the G pt . B be on E , and the st .
line BC on EF , the pt . c shall coincide with F , because BC = EF . ( Hyp . ) 2 .
Now bc coinciding with EF , AB , AC shall also coincide with DE , DF . For if AB ,
AC ...
Σελίδα 29
Let ABC , DEF be two as , having the sides AB , AC = to the two sides DE , DF ,
each to each ; likewise let the base BC = base EF ; then 2 BAC shall be = L EDF .
DEMONST . — ( By supraposition ) . 1 . For if the a ABC be applied to the a DEF ...
Let ABC , DEF be two as , having the sides AB , AC = to the two sides DE , DF ,
each to each ; likewise let the base BC = base EF ; then 2 BAC shall be = L EDF .
DEMONST . — ( By supraposition ) . 1 . For if the a ABC be applied to the a DEF ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent alternate applied base BC bisect called coincide common Const construction contained Deducible definition demonstration describe diam diameter divide draw Enun ENUN.-If ENUN.-Let ABC ENUN.—Let equal equilateral Euclid exterior extremity figure formed four given point greater Hence interior intersect isosceles join length less line drawn manner meet opposite sides parallel parallelogram position Post PROB produced proof Prop Proposition proved rectilineal remaining respectively right angles side ac square straight line student subtraction THEOR Theorem third trapezium triangle vertical Wherefore XXIX XXXI XXXII XXXIV
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.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope |
| Συγγραφέας | Euclides |
| Επιμελητής | William Trollope |
| Εκδόθηκε | 1847 |
| Πρωτότυπο από | Πανεπιστήμιο Οξφόρδης |
| Ψηφιοποιήθηκε στις | 3 Οκτ. 2006 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |