The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 51
... intersection of tʊo loci . ) Ex . 39. - If any straight line be drawn through the mid - point of the join of two fixed points , it is equidistant from them . DEF . - Parallel straight lines are such as are Book I. Prop . 26 . 51.
... intersection of tʊo loci . ) Ex . 39. - If any straight line be drawn through the mid - point of the join of two fixed points , it is equidistant from them . DEF . - Parallel straight lines are such as are Book I. Prop . 26 . 51.
Página 52
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . The symbol for ' parallel ' is PROPOSITION 27. THEOREM . If a straight line falling on two other straight lines ...
... Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . The symbol for ' parallel ' is PROPOSITION 27. THEOREM . If a straight line falling on two other straight lines ...
Página 53
... parallel . Let the st . line EF falling on the two st . lines AB , CD make ext . EGB equal to int . and opp . GHD on the same side , or make the two int . s on the same side , BGH , GHD , together equal to two rt . s ; then AB shall be ...
... parallel . Let the st . line EF falling on the two st . lines AB , CD make ext . EGB equal to int . and opp . GHD on the same side , or make the two int . s on the same side , BGH , GHD , together equal to two rt . s ; then AB shall be ...
Página 54
... parallel straight lines , it makes the alternate angles equal , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together equal to two right angles ...
... parallel straight lines , it makes the alternate angles equal , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together equal to two right angles ...
Página 55
... parallel to the same straight line , ' or ' Through a given point only one parallel can be drawn to a given straight line , ' from either of which Euclid's so - called ' 12th Axiom ' can be deduced . On the nature of this assumption see ...
... parallel to the same straight line , ' or ' Through a given point only one parallel can be drawn to a given straight line , ' from either of which Euclid's so - called ' 12th Axiom ' can be deduced . On the nature of this assumption see ...
Otras ediciones - Ver todas
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Sin vista previa disponible - 2015 |
Términos y frases comunes
bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices
Pasajes populares
Página 21 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 369 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Página 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Página 96 - 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.
Página 40 - Any two sides of a triangle are together greater than the third side.
Página 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Página 407 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Página 156 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...