The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 313
... Ratio , and Taylor circles ) . 6. The Brocard circle . The first three of these have been discussed at length in IV . 4 , 5 , and the notes appended thereto . The theorem involved in the definition of the fourth — the nine - point ...
... Ratio , and Taylor circles ) . 6. The Brocard circle . The first three of these have been discussed at length in IV . 4 , 5 , and the notes appended thereto . The theorem involved in the definition of the fourth — the nine - point ...
Página 318
... RATIO , AND TAYLOR'S CIRCLES . PROP . 6. The locus of the mid - points of anti - parallels to a side of a triangle with respect to the opposite vertex is a straight line . The proof is left as an exercise to the student . ( Compare Ex ...
... RATIO , AND TAYLOR'S CIRCLES . PROP . 6. The locus of the mid - points of anti - parallels to a side of a triangle with respect to the opposite vertex is a straight line . The proof is left as an exercise to the student . ( Compare Ex ...
Página 320
... Ratio Circle of the triangle ABC . It is also sometimes spoken of as the First Lemoine Circle . α M PROP . 9. — If ẞv , yλ , aμ be the anti - parallels obtained by joining the mid - points L , M , N of the sides of the pedal triangle ...
... Ratio Circle of the triangle ABC . It is also sometimes spoken of as the First Lemoine Circle . α M PROP . 9. — If ẞv , yλ , aμ be the anti - parallels obtained by joining the mid - points L , M , N of the sides of the pedal triangle ...
Página 328
... Ratio and Proportion . Book V. explains the terms used and establishes general theorems ; Book VI . applies these terms and theorems to plane figures . On account of the difficult nature of Book V. , it is usual to omit it from the ...
... Ratio and Proportion . Book V. explains the terms used and establishes general theorems ; Book VI . applies these terms and theorems to plane figures . On account of the difficult nature of Book V. , it is usual to omit it from the ...
Página 330
... ratio to one another when they can be multiplied so as to exceed the one the other . [ Rationem inter se habere magnitudines dicuntur quæ multiplicatæ altera alteram superare possunt .— ( Heiberg ) . ] In its usual form the definition ...
... ratio to one another when they can be multiplied so as to exceed the one the other . [ Rationem inter se habere magnitudines dicuntur quæ multiplicatæ altera alteram superare possunt .— ( Heiberg ) . ] In its usual form the definition ...
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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...