The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Σελίδα 32
... equilateral ABC ( Prop . I. ) , and bisect the ACB by the st . line CD ( Prop . IX . ) ; then AB is cut into two = A B D parts in the pt . D. DEMONST . - Because AC = CB , and CD is common to the △ ACD , BCD , .. the two sides AC , CD ...
... equilateral ABC ( Prop . I. ) , and bisect the ACB by the st . line CD ( Prop . IX . ) ; then AB is cut into two = A B D parts in the pt . D. DEMONST . - Because AC = CB , and CD is common to the △ ACD , BCD , .. the two sides AC , CD ...
Σελίδα 32
... equilateral △ DEF . ( Prop . I. ) Join cr ( Post . 1 ) . The st . line CF , drawn through the gn . pt . c , is at rt . s to AB . DEMONST . - 1 . Because DC = CE , and CF is common to the two As DCF , ECF ; .. the two sides DC , CF = EC ...
... equilateral △ DEF . ( Prop . I. ) Join cr ( Post . 1 ) . The st . line CF , drawn through the gn . pt . c , is at rt . s to AB . DEMONST . - 1 . Because DC = CE , and CF is common to the two As DCF , ECF ; .. the two sides DC , CF = EC ...
Σελίδα 62
... equilateral or isosceles triangle , a straight line be drawn to the base , from the angle con- tained by the two equal sides , and bisecting the angle ; it shall also bisect the base ; or if it bisect the base , it shall also bisect the ...
... equilateral or isosceles triangle , a straight line be drawn to the base , from the angle con- tained by the two equal sides , and bisecting the angle ; it shall also bisect the base ; or if it bisect the base , it shall also bisect the ...
Σελίδα 72
... equilateral △ is one - third of two rt . 4o , or two- thirds of a rt . ; and that if two of the angles of any △ are to two of the angles of another , the third of the other . The converse of thus partially enunciated and = the one is ...
... equilateral △ is one - third of two rt . 4o , or two- thirds of a rt . ; and that if two of the angles of any △ are to two of the angles of another , the third of the other . The converse of thus partially enunciated and = the one is ...
Σελίδα 73
... of the rt . ; .. also , the △ ABD = LDBE = LEBC . A D E C of an equilateral △ ) = rds of a rt . ≤ ; DBE , EBC ( by construction ) = 3rd of a rd of a rt . ; .. 2 ABD = Н Wherefore the rt . ABC has been trisected by the PROP . XXXII . 73.
... of the rt . ; .. also , the △ ABD = LDBE = LEBC . A D E C of an equilateral △ ) = rds of a rt . ≤ ; DBE , EBC ( by construction ) = 3rd of a rd of a rt . ; .. 2 ABD = Н Wherefore the rt . ABC has been trisected by the PROP . XXXII . 73.
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.