The first book of Euclid's Elements, simplified, explained and illustrated, by W. Trollope1847 |
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Resultat 1-5 av 16
Side 3
... third definition will , mutatis mutandis , equally apply here ; spherical or curved superficies or surfaces ( super and facies ) , which have no boundaries , not being taken into consideration . It will also materially conduce to a ...
... third definition will , mutatis mutandis , equally apply here ; spherical or curved superficies or surfaces ( super and facies ) , which have no boundaries , not being taken into consideration . It will also materially conduce to a ...
Side 18
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each ; viz . those to which the equal sides are opposite . PART . ENUN . - Let ABC , DEF , be two As , which have the two sides ...
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each ; viz . those to which the equal sides are opposite . PART . ENUN . - Let ABC , DEF , be two As , which have the two sides ...
Side 26
... third case , in which the vertex of one A is upon a side of the other , needs no demon- stration . ( See figure to Prop . VI . ) Wherefore , upon the same base , and on the same side of it , & c . - Q . E. D. In the same way it may be ...
... third case , in which the vertex of one A is upon a side of the other , needs no demon- stration . ( See figure to Prop . VI . ) Wherefore , upon the same base , and on the same side of it , & c . - Q . E. D. In the same way it may be ...
Side 28
... third case , in which the vertex of one △ is upon a side of the other , needs no demon- stration . ( See figure to Prop . VI . ) Wherefore , upon the same base , and on the same side of it , & c . - Q . E. D. In the same way it may be ...
... third case , in which the vertex of one △ is upon a side of the other , needs no demon- stration . ( See figure to Prop . VI . ) Wherefore , upon the same base , and on the same side of it , & c . - Q . E. D. In the same way it may be ...
Side 48
... third side . BC , AB + BC > AC , PART . ENUN . - Let ABC be any Δ . Then the sum of any two of its sides is the third side , viz . , BA + AC is and BCCA > AB . CONST . - Produce BA to the pt . D ( Post . 2 ) , making AD AC . ( Prop ...
... third side . BC , AB + BC > AC , PART . ENUN . - Let ABC be any Δ . Then the sum of any two of its sides is the third side , viz . , BA + AC is and BCCA > AB . CONST . - Produce BA to the pt . D ( Post . 2 ) , making AD AC . ( Prop ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 9 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Side 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.
Side 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...
Side 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.
Side 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.