The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 178
... reqd . will lie on EO by Ex . 203 . Find C also so that the sum of the squares shall be a maximum . Ex . 279. — Find the greatest and least lines which can be drawn from any point on the circumference of a circle to any point on the ...
... reqd . will lie on EO by Ex . 203 . Find C also so that the sum of the squares shall be a maximum . Ex . 279. — Find the greatest and least lines which can be drawn from any point on the circumference of a circle to any point on the ...
Página 209
... reqd . to describe the of which ABC is a segment . Take any pt . B on the arc ABC , and join AB , BC , and bisect AB , BC in D and E. Through D and E draw rs to AB , BC . These rs must both pass through the centre , .. they must , if ...
... reqd . to describe the of which ABC is a segment . Take any pt . B on the arc ABC , and join AB , BC , and bisect AB , BC in D and E. Through D and E draw rs to AB , BC . These rs must both pass through the centre , .. they must , if ...
Página 215
... reqd . to bisect it . Join AB and bisect it in C ; from C draw CD r to AB to cut the arc in D : then arc ADB is bisected at D. Join AD , BD . In As ACD , BCD , AC , CD = BC , CD , A and rt . 4 ACD = rt . 4 BCD ; ... AD = DB , and each ...
... reqd . to bisect it . Join AB and bisect it in C ; from C draw CD r to AB to cut the arc in D : then arc ADB is bisected at D. Join AD , BD . In As ACD , BCD , AC , CD = BC , CD , A and rt . 4 ACD = rt . 4 BCD ; ... AD = DB , and each ...
Página 220
... reqd . to describe on AB a segt . of a containing an equal to C. Bisect AB at F. ( 1 ) If C is a rt . 4 , with centre F and rad . FA or FB , describe the semi - O АНВ . Then AHB is a rt . 4 , ( 2 ) If .. AHB = LC . C be not a rt ...
... reqd . to describe on AB a segt . of a containing an equal to C. Bisect AB at F. ( 1 ) If C is a rt . 4 , with centre F and rad . FA or FB , describe the semi - O АНВ . Then AHB is a rt . 4 , ( 2 ) If .. AHB = LC . C be not a rt ...
Página 274
... reqd . to place in ABC a st . line equal to D. Draw any diamr . BC . If BC = D , the prob . is solved . If not , from CB cut off CE equal to D. 이 With centre C and radius CE describe a cutting ABC in A. Join AC AC shall be the line reqd ...
... reqd . to place in ABC a st . line equal to D. Draw any diamr . BC . If BC = D , the prob . is solved . If not , from CB cut off CE equal to D. 이 With centre C and radius CE describe a cutting ABC in A. Join AC AC shall be the line reqd ...
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...