The third Question in Double Fellowship, page 189, read að follows. Six merchants trade after this manner. A puts in gol. for 6 months, and 6ol. for 4 months. B puts in gol. for 8 months. C puts in 160l, for 5 months, and 100l. for 4 month. D puts in 2001. for 7 months, and 100l for 5 months E-puts in 300l. for 10 months, and 100l. for 2months. F puts in 400l. for 3 months, 200l. for 4 months, and 2001. for 5 months. They gained 686,41. what is the fhare of each merchant. 45. ·2529 -6144 32072 61443-2 12285048 1.499500.. J.. 3 614432048 6144-3-2-1, Note, b denotes from the bottom. The Reader is defired to Correct thefe i INTRODUCTION, ATHEMATICS originally fignified any dif Mcipline or learning, (Mathefits:) But now it is that fcience which contemplates and treats of all kinds of quantities that are capable of being numbered or measured. That part which relates to number only, is called Arithmetic; and that which relates to measure in general, whe ther length, breadth, motion, force, &c. is called Geometry. When these two are converfant about multitude and magnitude abstractedly confidered, they are called pure or abstract Mathematics, and are the foundation of all the other parts. When they are applied to particular fubjects, they are called mixt Mathematics. Mathematics are alfo called fpeculative, so far as they are concerned in finding out true propofitions; and practical, as they relate to ufe, and are applied to practice. QUANTITY is whatever will admit of augmentation and diminution; or is capable of any fort of estimation or mensuration. A PROPOSITION is fomething propofed to be proved or demonstrated. A THEOREM is a demonftrable propofition laid down as an acknowledged truth; and a fet of fuch theo rems is called a Theory. A PROBLEM is a queftion requiring fomething to be done. A limited Problem is that which has but one anfwer. An unlimitted Problem is that which has an infinite number of anfwers. A determinate Problem is that which has a certain number of anfwers. A SOLUTION of a Problem is the answer given to it. A numerical Solution is the answer in numbers. geometrical Solution is an answer by the principles of Geometry. A mechanical Solution is one which is gained by trials. A LEMMA fignifies a propofition, which ferves previously to prepare the way for the more easy apprehension of the demonftration of fome Theorem. A CORROLLARY, or Confectary, is a confequence drawn from a propofition already demonftrated. A SCHOLIUM is a remark made on any propofition, corrollary or discourse. PRINCIPLES are the firft grounds, rules, or foundations, of any Science; as Definitions, Axioms, Poftulates, and Hypothefes. A DEFINITION is our explication of any word or term in any Science; which explication ought to be clear, and to contain no word or term, but what is already understood. An AXIOM, or Maxim, is fuch a common, plain, felf-evident propofition, as nobody can deny without contradicting common fenfe and reason. And nothing ought to be allowed for an Axiom but what is thus clear and felf evident: as, that nothing can act where it is not; that a thing cannot be, and not be, at the fame time; that the whole is greater than a part thereof; that no body can naturally go into nothing: Out of an infinite number of felf evident truths that occur occur to the mind, men felect fuch as are general, and of moff ufe in demonstrating any science, and lay them up in ftore to have recourse to, as need requires. And tho' in their reafoning they do not always mention fuch and fuch Axioms; yet the mind perceives the force of them, without ftopping to hear them particularly repeated or named.. A POSTULATE, or Petition, is fomething required to be granted, which is too evident to be denied. An HYPOTHESIS is a fuppofition affumed to be true, by which a man is to argue, and build his reasoning upon. DEMONSTRATION, is a hain of arguments depending on one another, and founded primarily on first and felf evident Principles, or plain Propofitions efta-.. blished and proved from them, and at laft ending in the invincible proof of the thing to be demonftrated. METHOD is the art of difpofing a train of arguments, in right order, either to find out the truth, or faliehood of a Propofition; or to demonftrate it to ethers when we have found it out. This is either analytical' or fynthetical. ANALYSIS, or the Analytic Method, is the art of finding out the truth of a Propofition, by fuppofing the thing to be done; and going back ftep by step, till we arrive at fome known truth. This is called the method of invention, and is generally used in Algebra. SYNTHESIS, or the Synthetic Method, is the fearching out truth, by firft laying down fome fimple and eafy principles, and purfuing the confequences till we come at This method begins at the most fimple the conclufion. A 2 and |