The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 30.
Σελίδα 5
... coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . II . All right angles are equal to one another ...
... coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . II . All right angles are equal to one another ...
Σελίδα 12
... coincide with the point E , because AB is equal to DE ; [ HYP . And AC will fall on DF , because the angle BAC is equal to the angle EDF ; therefore also the point C will coincide with the point F , because AC is equal to DF ; [ HYP ...
... coincide with the point E , because AB is equal to DE ; [ HYP . And AC will fall on DF , because the angle BAC is equal to the angle EDF ; therefore also the point C will coincide with the point F , because AC is equal to DF ; [ HYP ...
Σελίδα 13
... coincides with the whole triangle DEF , and is equal to it . [ AX . 8 . Also since AB , BC coincide with DE , EF , therefore the angle B is equal to the angle E. [ AX . 8 . And since AC , CB coincide with DF , FE , therefore the angle C ...
... coincides with the whole triangle DEF , and is equal to it . [ AX . 8 . Also since AB , BC coincide with DE , EF , therefore the angle B is equal to the angle E. [ AX . 8 . And since AC , CB coincide with DF , FE , therefore the angle C ...
Σελίδα 20
... coinciding with EF , BA and AC will coincide with ED and DF . For if not , on EF as base there will be another triangle formed on the same side of it as DEF , and having the side terminated at E equal to DE , and also the side ...
... coinciding with EF , BA and AC will coincide with ED and DF . For if not , on EF as base there will be another triangle formed on the same side of it as DEF , and having the side terminated at E equal to DE , and also the side ...
Σελίδα 49
... D must lie somewhere on the straight line . from C through A , FLC ; .. it must coincide with A , [ HYP . and .. the whole △ DEF coincides with the whole A ABC and = it , and AB = DE , and AC = DF , Book I. Prop . 26 . 49.
... D must lie somewhere on the straight line . from C through A , FLC ; .. it must coincide with A , [ HYP . and .. the whole △ DEF coincides with the whole A ABC and = it , and AB = DE , and AC = DF , Book I. Prop . 26 . 49.
Άλλες εκδόσεις - Προβολή όλων
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Σελίδα 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 40 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...