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absurd admit angle answer argument arithmetical value assertion assume attempt Book centre chord circle of diameter circle X circumference circumscribing square communication conclusion construction contain the right correspondence dear Sir December decimals demonstrated denote determinate diagonals 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 radii radius ratio reasoning reference represented result right-angled triangle self-evident sides similar sine square straight line subtending Tables tell theorem trigonometrical true truth
Page 39 - 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 279 - 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 116 - 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 152 - 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 278 - Seldom has that kind of royalty been quietly conceded to any man of genius until his tomb becomes his throne and yet there is not one of us now present who thinks it strange that it is granted without a murmur to the guest whom we receive tonight.
Page 278 - Happy is the man who makes clear his title-deeds to the royalty of genius while he yet lives to enjoy the gratitude and reverence of those whom he has subjected to his sway. Though it is by conquest that he achieves his throne, he at least is a conqueror whom the conquered bless ; and the more despotically he enthralls, the dearer he becomes to the hearts of men.
Page 362 - ... other from his writings. His lively sallies on this subject much amused the Empress, and all the younger part of her Court. But some of the older courtiers suggested that it was hardly prudent to allow such unreserved exhibitions. The Empress thought so too, but did not like to muzzle her guest by an express prohibition: so a plot was contrived. The scorner was informed that an eminent mathematician had an algebraical proof of the existence of God, which he would communicate before the whole...
Page i - ... 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...