Cambridge University Press по журналам "Mathematical Notes"
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(Cambridge University Press. Cambridge, UK, 19140101)The following method of cutting off an nth part of a given straight line requires besides a ruler only a pair of dividers or other means of laying off on a given straight line a segment equal to the distance between two ...

(Cambridge University Press. Cambridge, UK, 19150101)The instrument is an ordinary dry and wet bulb hygrometer adapted to give a direct reading of the percentage humidity. I, I are pointers set at the dry and wet bulb readings by means of pieces sliding on the rods A, B and ...

(Cambridge University Press. Cambridge, UK, 19091201)A big stumblingblock in the way of the child beginning Algebra is the transition from the conception of definite numbers in Arithmetic to that of indefinite quantities in Algebra, and the performance on these of the ...

(Cambridge University Press. Cambridge, UK, 19290101)The following two propositions are converses of Euclid III., 11 and 12. Prop. 1. If the circumferences of two circles whose centres are A and B have a common point C lying in the straight line AB, then the circles touch ...

(Cambridge University Press. Cambridge, UK, 19350101)§ 1. Chowla has generalised Wolstenholme's Theorem as follows: where p denotes as usual a prime, and < is used for “less than and prime to.”

(Cambridge University Press. Cambridge, UK, 19330101)The Diagram shows two complete, and one partially complete, concentric circles. The radii of the largest and smallest are as four to one respectively.

(Cambridge University Press. Cambridge, UK, 19300101)The following proof is designed to link up Hero's formula geometrically with the formulae for the trigonometrical functions of ½A in a triangle.

(Cambridge University Press. Cambridge, UK, 19301001)(1) Apparently it was in 1854 that Hermite first drew attention to the special determinant which now bears his name. It may be defined as being such that every two of its elements that are conjugate in position are ...

(Cambridge University Press. Cambridge, UK, 19111001)To determine logarithms to the base 1·1.—If N = ax, x is the logarithm of N to the base a. Hence, if N = 1·1x, x is the logarithm of N to the base 1·1, and, by plotting different values of x with the corresponding values ...

(Cambridge University Press. Cambridge, UK, 19090701)Draw axes XOX′, YOY′. Draw graph of y = φ(t), taking OX as a positive axis of t. (In Figure see dotted line). Draw graph of x =f(t), taking OY′ as positive axis of t. (In Figure f(t) = t3 – t2; see broken line). Take any ...

(Cambridge University Press. Cambridge, UK, 19160401)In the ordinary textbooks on Algebra there is a lack of suitable examples on Multiplication of Determinants. Most of the examples that are given are particular cases of the theorem where A1 A2, …, B1, …, are the cofactors ...

(Cambridge University Press. Cambridge, UK, 19601201)

(Cambridge University Press. Cambridge, UK, 19240501)Let O be the centre of the circumscribing circle of ΔABC, A1 the middle point of BC, and EA1OF the diameter at right angles to BC. Draw AX perpendicular to BC and produce it to meet the circle in K. Let H be the orthocentre ...

(Cambridge University Press. Cambridge, UK, 19240501)Girard enunciated in 1625 the following celebrated theorem, which is associated with the name of Fermat: Every prime of the form 4m + 1 is the sum of two squares in one way only, and no prime of the form 4m  1 is a factor ...

(Cambridge University Press. Cambridge, UK, 19101201)The following apparatus for verifying Boyle's Law in an elementary manner is of interest from the point of view of pure mathematics as well as that of the laboratory. The method of construction, which I have described in ...

(Cambridge University Press. Cambridge, UK, 19611201)

(Cambridge University Press. Cambridge, UK, 19140501)Consider the curve y = ae−t/t0 (Fig. 1.) Mark off along the t – axis a distance OT0 equal to the time constant t0. Divide OT0 into n equal parts and erect ordinates at each point of division. M, N, are the mth and (m + ...

(Cambridge University Press. Cambridge, UK, 19110401)Let ABCD be a horizontal section of a rectangular slab of glass. A pin is set up vertically at P, close to the face AB, or at a short distance from it. It is possible to see the pin P through the glass if we look through ...

(Cambridge University Press. Cambridge, UK, 19120501)It is proposed to trace the curves represented by the equation for the values of a (i) a = 2, (ii) a = 1.

(Cambridge University Press. Cambridge, UK, 19130501)An application of the method of Induction to the proof of a general result or theorem should involve two steps: (i) the discovery of the result to be proved by the consideration of particular cases; (ii) a proof, by ...
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