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admit angle answer argument arithmetical value assertion assume Athenĉum attempt Book centre chord circle of diameter circle X circumference circumscribing square communication conclusion construction contain the right correspondence dear Sir decimals demonstrated denote determinate diagram diameter diameter unity difference direction enclosed equal equation Euclid exactly equal expression fact Fault finite follows four geometrical give given greater half Hence hexagon hypothenuse hypothesis inscribed interval JAMES SMITH join length less Letter Logarithm Mathematics mean proportional meet miles Morgan natural sine never November observe parallelogram perimeter Produce PROFESSOR WHITWORTH proof Prop prove quantity question radius ratio reasoning reference regular inscribed represented result right-angled triangle self-evident sides similar sine square straight line subtending Tables tell theorem trigonometrical true truth
Page 47 - 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.
Page 140 - I have often said, that this world is a comedy to those who think, a tragedy to those who feel ; and sensibility has not only occasion to suffer for others, but is sure of its own portion too.
Page 174 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 301 - tis not so deep as a well, nor so wide as a church door ; but 'tis enough, 'twill serve : ask for me to-morrow, and you shall find me a grave man. I am peppered, I warrant, for this world. A plague o...
Page 136 - If the radius of a circle is 12, find the difference between the area of the circle and the area of the inscribed square.
Page 174 - ... 2. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts are together equal to the square on the.
Page 1 - ... equal to the right angles in the others, and the angle at C forms the angle at the base to every one of the three triangles, that is, it is common to all the three ; and as all the angles of a plane triangle are together equal to two right angles (Art. 5) the remaining or third angle must be equal in all the triangles ; for that angle is the complement (Art. 5) of the angle at C in each of the triangles. Now all plane triangles which are equiangular, have the sides which contain the corresponding...
Page 106 - The angle at the centre of a circle, subtended by an arc, is double the angle at the circumference subtended by the same arc.
Page 387 - Goldsmith could not have seen the anecdote, or he might have been supposed to have drawn from it a hint as to the way in which the Squire demolished poor Moses. The graphomath is a person who, having no mathematics, attempts to describe a mathematician. Novelists perform in this way : even Walter Scott now and then burns his fingers. His dreaming calculator, Davy Ramsay, swears 'by the bones of the immortal Napier.