The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Página 11
... Theorem , easily capable of proof , but certainly requir- ing one . A proof is appended to the 29th Proposition . N. B. - The " Elements " of Euclid are set forth in a series of Propositions , of which there are two forms , viz.:- the ...
... Theorem , easily capable of proof , but certainly requir- ing one . A proof is appended to the 29th Proposition . N. B. - The " Elements " of Euclid are set forth in a series of Propositions , of which there are two forms , viz.:- the ...
Página 17
... But , by construction AE = BD ; ... also AC BC ( Ax . 1 ) . Hence the △ ABC is isosceles , and it has been described upon the gn . straight line AB.-Q. E. F. F Fig . 2 . C DA BE PROP . IV . THEOREM . GEN . ENUN . PROP . III . 17.
... But , by construction AE = BD ; ... also AC BC ( Ax . 1 ) . Hence the △ ABC is isosceles , and it has been described upon the gn . straight line AB.-Q. E. F. F Fig . 2 . C DA BE PROP . IV . THEOREM . GEN . ENUN . PROP . III . 17.
Página 18
Euclides William Trollope. PROP . IV . THEOREM . GEN . ENUN . - If two triangles have two sides of the one equal to two sides of the other , each to each , and have also the angles contained by those sides equal , they shall likewise ...
Euclides William Trollope. PROP . IV . THEOREM . GEN . ENUN . - If two triangles have two sides of the one equal to two sides of the other , each to each , and have also the angles contained by those sides equal , they shall likewise ...
Página 26
... theorem for the sole purpose of proving the next , to which it may therefore be considered as a Lemma ; i . e . a proposition which is merely prepa- ratory to the demonstration of another . The limitation that the two triangles should ...
... theorem for the sole purpose of proving the next , to which it may therefore be considered as a Lemma ; i . e . a proposition which is merely prepa- ratory to the demonstration of another . The limitation that the two triangles should ...
Página 28
... theorem for the sole purpose of proving the next , to which it may therefore be considered as a Lemma ; i . e . a proposition which is merely prepa- ratory to the demonstration of another . The limitation that the two triangles should ...
... theorem for the sole purpose of proving the next , to which it may therefore be considered as a Lemma ; i . e . a proposition which is merely prepa- ratory to the demonstration of another . The limitation that the two triangles should ...
Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Página 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.
Página 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...
Página 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.
Página 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.