The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Seite 65
... . DEMONST . - 1 . Because the AGH = vertical 4 A C E B G F D EGB ( Prop . XV . ) = GHD ( Hyp . ) , and they are alternates ; .. AB is | to CD . ( Prop . XXVII . ) 2. Again , because the S AGH + BGH = PROP . XXVIII . 65.
... . DEMONST . - 1 . Because the AGH = vertical 4 A C E B G F D EGB ( Prop . XV . ) = GHD ( Hyp . ) , and they are alternates ; .. AB is | to CD . ( Prop . XXVII . ) 2. Again , because the S AGH + BGH = PROP . XXVIII . 65.
Seite 66
... alternate < s ; .. AB is to CD . ( Prop . XXVII . ) Wherefore , if a st . line , & c . - Q . E. D. PROP . XXIX . THEOR . GEN . ENUN . - If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to ...
... alternate < s ; .. AB is to CD . ( Prop . XXVII . ) Wherefore , if a st . line , & c . - Q . E. D. PROP . XXIX . THEOR . GEN . ENUN . - If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to ...
Seite 68
... ENUN . - Let AB , CD be both to EF ; then AB is || to CD . CONST . - Let the st . line GHK cut AB , ef , cd . DEMONST . - 1 . Because AB is to EF , and GHK cuts A B H E K C- them , .. the AGH = alternate GHF . ( 68 -BOOK I. EUCLID.-
... ENUN . - Let AB , CD be both to EF ; then AB is || to CD . CONST . - Let the st . line GHK cut AB , ef , cd . DEMONST . - 1 . Because AB is to EF , and GHK cuts A B H E K C- them , .. the AGH = alternate GHF . ( 68 -BOOK I. EUCLID.-
Seite 69
... alternate s ; .. AB is || to CD . Wherefore , st . lines , & c . - Q . E. D. It is clear that the 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 ...
... alternate s ; .. AB is || to CD . Wherefore , st . lines , & c . - Q . E. D. It is clear that the 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 ...
Seite 70
... alternate DCG ( Prop . XXIX . ) ; the verti- cal EDB = vertical CDG E of any number A C B D F ( Prop . XV . ) ; and the side BD = DC ( Hyp . ) ; . ' . △ ebd A GCD ( Prop . XXVI . ) , and < than △ CDF . = 2. To each add the trapezium ...
... alternate DCG ( Prop . XXIX . ) ; the verti- cal EDB = vertical CDG E of any number A C B D F ( Prop . XV . ) ; and the side BD = DC ( Hyp . ) ; . ' . △ ebd A GCD ( Prop . XXVI . ) , and < than △ CDF . = 2. To each add the trapezium ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Seite 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.
Seite 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...
Seite 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.
Seite 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.