The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope |
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Σελίδα 69
... same reasoning may be carried on to any number of lines ; nor is it necessary
that EF should lie between AB and cd ; and the student should prove the
Theorem , when it is placed either above ab or below cd . PROP . XXXI . THEOR .
GEN .
... same reasoning may be carried on to any number of lines ; nor is it necessary
that EF should lie between AB and cd ; and the student should prove the
Theorem , when it is placed either above ab or below cd . PROP . XXXI . THEOR .
GEN .
Σελίδα 70
D . Let the base bc of the A ABC be bisected in D ; also let AEF be any other A ,
having the same vertical Z , and whose base passes through D . The A ABC is <
than the A AEF . DEMONST , - 1 . Throughc B4 draw cg | | to AB ( Prop . XXXI . ) ...
D . Let the base bc of the A ABC be bisected in D ; also let AEF be any other A ,
having the same vertical Z , and whose base passes through D . The A ABC is <
than the A AEF . DEMONST , - 1 . Throughc B4 draw cg | | to AB ( Prop . XXXI . ) ...
Σελίδα 74
Const . - Upon AB describe an equilateral A ABC ( Prop . I . ) ; bi . sect the 48 CAB
, CBA by the st . lines AD , BD , meeting in D ( Prop . IX . ) ; through D draw DE | |
to AC , and DF | | to BC ( Prop . XXXI . ) ; then AB will be trisected in the pts .
Const . - Upon AB describe an equilateral A ABC ( Prop . I . ) ; bi . sect the 48 CAB
, CBA by the st . lines AD , BD , meeting in D ( Prop . IX . ) ; through D draw DE | |
to AC , and DF | | to BC ( Prop . XXXI . ) ; then AB will be trisected in the pts .
Σελίδα 84
BE and ch are also = and | | ( Prop . XXXI . ) ; and . . . EBCH is a om . ( Prop .
XXXIV . Def . ) 3 . Now , because the oms ABCD , EBCH are upon the same base
BC , and between the same | | S AH , BC , . . Om ABCD = Om EBCH . ( Prop .
XXXV . ) ...
BE and ch are also = and | | ( Prop . XXXI . ) ; and . . . EBCH is a om . ( Prop .
XXXIV . Def . ) 3 . Now , because the oms ABCD , EBCH are upon the same base
BC , and between the same | | S AH , BC , . . Om ABCD = Om EBCH . ( Prop .
XXXV . ) ...
Σελίδα 85
XXXI . ) ; and through E draw En also 11 to Ac , meeting AB produced in 1 . Then
AHCE is a om between the same 11 % with the trapezium ABCD , of which the
base CE = CD + DE = CD + AB ( Const . ) ; and the trapezium ABCD = _ OM ...
XXXI . ) ; and through E draw En also 11 to Ac , meeting AB produced in 1 . Then
AHCE is a om between the same 11 % with the trapezium ABCD , of which the
base CE = CD + DE = CD + AB ( Const . ) ; and the trapezium ABCD = _ OM ...
Τι λένε οι χρήστες - Σύνταξη κριτικής
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 |