The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Σελίδα 13
... side of AB , another equilateral △ ABF , may in like manner be described ; and if CF be joined , the As ACF , BCF are isos- celes , having the base , or under side , longer than either of the two equal sides AC , AF , and BC , BF . A ...
... side of AB , another equilateral △ ABF , may in like manner be described ; and if CF be joined , the As ACF , BCF are isos- celes , having the base , or under side , longer than either of the two equal sides AC , AF , and BC , BF . A ...
Σελίδα 15
... BC ( AX . 1 ) . .. by sub- Wherefore , from the gn . pt . A , a st . line AL has been drawn equal to the gn . st ... side of the A ; -not their difference . Since then the gn . pt . may be joined to either extremity of the gn ...
... BC ( AX . 1 ) . .. by sub- Wherefore , from the gn . pt . A , a st . line AL has been drawn equal to the gn . st ... side of the A ; -not their difference . Since then the gn . pt . may be joined to either extremity of the gn ...
Σελίδα 21
... side of the base . Therefore the s at the base , & c . — Q . E. D. COROLLARY . - Hence every equilateral △ is also ... BC , . ' . △ BAC ACB ; .. the ABC , ACB , BAC , are equal : i.e. the ABC is equiangular . - Q . E. D. C Partly ...
... side of the base . Therefore the s at the base , & c . — Q . E. D. COROLLARY . - Hence every equilateral △ is also ... BC , . ' . △ BAC ACB ; .. the ABC , ACB , BAC , are equal : i.e. the ABC is equiangular . - Q . E. D. C Partly ...
Σελίδα 23
Euclides William Trollope. Since in AS DBC , ACB , the side DB = AC , and BC is common to both , ... the two DB , BC = the two AC , CB , each to each ; and the DBC = ACB ( Hyp . ) ; .. base DC = base AB , and the area of DBC area of ...
Euclides William Trollope. Since in AS DBC , ACB , the side DB = AC , and BC is common to both , ... the two DB , BC = the two AC , CB , each to each ; and the DBC = ACB ( Hyp . ) ; .. base DC = base AB , and the area of DBC area of ...
Σελίδα 24
... side AB shall the side AC . = CONST . - In BD take any pt . F , and from CE cut off CG = BF . ( Prop . III . ) Join BG , CF , FG . DEMONST . - 1 . Prove that the BCF LCBG . S F A B G E Because BF CG , and BC is common to the △ FBC ...
... side AB shall the side AC . = CONST . - In BD take any pt . F , and from CE cut off CG = BF . ( Prop . III . ) Join BG , CF , FG . DEMONST . - 1 . Prove that the BCF LCBG . S F A B G E Because BF CG , and BC is common to the △ FBC ...
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.