The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 84.
Σελίδα 27
... Show that AP is equal to BP . Ex . 8. - A and B are two given points , and C the mid - point of their join ; P is any other point such that AP is equal to BP . Show that CP is r to AB . N.B.-Ex. 7 and 8 are particular enunciations of ...
... Show that AP is equal to BP . Ex . 8. - A and B are two given points , and C the mid - point of their join ; P is any other point such that AP is equal to BP . Show that CP is r to AB . N.B.-Ex. 7 and 8 are particular enunciations of ...
Σελίδα 41
... Show that the perimeter of the hexagon is greater than half the sum of the perimeters of the triangles . Ex . 31. - ABCDEF is a hexagon . Show that its perimeter is greater than two - thirds of the sum of the three diagonals AD , BE ...
... Show that the perimeter of the hexagon is greater than half the sum of the perimeters of the triangles . Ex . 31. - ABCDEF is a hexagon . Show that its perimeter is greater than two - thirds of the sum of the three diagonals AD , BE ...
Σελίδα 43
... Show that the outside path is the longer . B ( A generalisation of the first part of Prop . 21 , to be proved in the same way . ) Examine the effect of omitting the words in italics from the hypothesis . Ex . 33. - O is any point within ...
... Show that the outside path is the longer . B ( A generalisation of the first part of Prop . 21 , to be proved in the same way . ) Examine the effect of omitting the words in italics from the hypothesis . Ex . 33. - O is any point within ...
Σελίδα 62
... show that the whole amount of turning will be greater than if it were to slide in the same manner along the inside ... Show that six equal regular triangles can be arranged round one common vertex , so as to make a regular hexagon . Ex ...
... show that the whole amount of turning will be greater than if it were to slide in the same manner along the inside ... Show that six equal regular triangles can be arranged round one common vertex , so as to make a regular hexagon . Ex ...
Σελίδα 65
... show that BGC is one - third of AABC . Hence , show that median CF also passes through G. When any number of st . lines pass through the same point they are said to be concurrent . Note that the three medians of a triangle are ...
... show that BGC is one - third of AABC . Hence , show that median CF also passes through G. When any number of st . lines pass through the same point they are said to be concurrent . Note that the three medians of a triangle are ...
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...