The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 σελίδες |
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Σελίδα 13
... respectively equal to the sides PQ , QR , RS , and the angles B and C respectively equal to the angles Q and R. Show that the quadrilaterals are congruent . DEF . A triangle with two of its sides equal to each other is called an ...
... respectively equal to the sides PQ , QR , RS , and the angles B and C respectively equal to the angles Q and R. Show that the quadrilaterals are congruent . DEF . A triangle with two of its sides equal to each other is called an ...
Σελίδα 18
... AD to E and F respectively . Then because AC is equal to AD , [ HYP . therefore the angle ECD is equal to the angle FDC ; [ I. 5 . But the angle ECD is greater than the angle BCD 18 Euclid's Elements . PROPOSITION 7. THEOREM. ...
... AD to E and F respectively . Then because AC is equal to AD , [ HYP . therefore the angle ECD is equal to the angle FDC ; [ I. 5 . But the angle ECD is greater than the angle BCD 18 Euclid's Elements . PROPOSITION 7. THEOREM. ...
Σελίδα 33
... EA , EC , EB , ED be drawn from a point E , making the LS AEC , CEB respectively equal to their opposite BED , DEA , they form two st . lines AB , CD . s PROPOSITION 16. THEOREM . If one side of a triangle Book I. Prop . 15 . 33.
... EA , EC , EB , ED be drawn from a point E , making the LS AEC , CEB respectively equal to their opposite BED , DEA , they form two st . lines AB , CD . s PROPOSITION 16. THEOREM . If one side of a triangle Book I. Prop . 15 . 33.
Σελίδα 34
... respectively , and AEB = 4 CEF . L .. 4 BAE = L ECF . But ACD > < ECF . ... LACD > < BAC . [ CONST . [ I. 15 . [ I. 4 . [ AX . 9 . In the same manner , if BC be bisected and the side AC pro- duced to G , it may be shown that BCG > < ABC ...
... respectively , and AEB = 4 CEF . L .. 4 BAE = L ECF . But ACD > < ECF . ... LACD > < BAC . [ CONST . [ I. 15 . [ I. 4 . [ AX . 9 . In the same manner , if BC be bisected and the side AC pro- duced to G , it may be shown that BCG > < ABC ...
Σελίδα 45
... respectively ; then 4 FAG = L DCE . [ I. 22 . [ I. 8 . NOTE . In Practical Geometry it is usual to make the two lines CD , CE equal ( by describing an arc with centre C and any radius ) ; and then to make a triangle FAG congruent with ...
... respectively ; then 4 FAG = L DCE . [ I. 22 . [ I. 8 . NOTE . In Practical Geometry it is usual to make the two lines CD , CE equal ( by describing an arc with centre C and any radius ) ; and then to make a triangle FAG congruent with ...
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...