The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Αποτελέσματα 1 - 5 από τα 59.
Σελίδα 5
Euclides William Trollope. coinciding with the plane of the paper , the line joining any two points , E and F , lies clearly within the superficies ; but in abcd , which stands out of the plane of the paper , the line joining E and F ...
Euclides William Trollope. coinciding with the plane of the paper , the line joining any two points , E and F , lies clearly within the superficies ; but in abcd , which stands out of the plane of the paper , the line joining E and F ...
Σελίδα 17
... join AC , BC ( Post . 1 ) . Then ABC is the △ required . DEMONST . - By the property of the O , AE AC , and BD = BC ( Def . 15 ) . But , by construction AE = BD ; ... also AC BC ( Ax . 1 ) . Hence the △ ABC is isosceles , and it has ...
... join AC , BC ( Post . 1 ) . Then ABC is the △ required . DEMONST . - By the property of the O , AE AC , and BD = BC ( Def . 15 ) . But , by construction AE = BD ; ... also AC BC ( Ax . 1 ) . Hence the △ ABC is isosceles , and it has ...
Σελίδα 20
... join FC , GB ( Post . 1 ) . DEMONST . - 1 . To prove the As AGB , AFC = in every respect . Because AF AG , and AB = AC ; .. the two sides FA , AC = two sides GA , AB , each to each . Also they contain mon to the two As AFC , AGB ; FAG ...
... join FC , GB ( Post . 1 ) . DEMONST . - 1 . To prove the As AGB , AFC = in every respect . Because AF AG , and AB = AC ; .. the two sides FA , AC = two sides GA , AB , each to each . Also they contain mon to the two As AFC , AGB ; FAG ...
Σελίδα 22
... B the < . ( Prop . III . ) Join DC ( Post . 1 ) . DEMONST . - 1 . Show the absurdity resulting from the above supposition ; viz . , that △ DBC would = △ ABC . Since in AS DBC , ACB , the side DB 22 BOOK I. EUCLID . -
... B the < . ( Prop . III . ) Join DC ( Post . 1 ) . DEMONST . - 1 . Show the absurdity resulting from the above supposition ; viz . , that △ DBC would = △ ABC . Since in AS DBC , ACB , the side DB 22 BOOK I. EUCLID . -
Σελίδα 24
... 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 , GCB , .. the two sides FB , BC = GC , CB , each to each ; and the contained / FBC = Z GCB ( Hyp . ) ; ... the ...
... 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 , GCB , .. the two sides FB , BC = GC , CB , each to each ; and the contained / FBC = Z GCB ( Hyp . ) ; ... the ...
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.