PRO 



PRO 



trine of Chances, is the ratio of the num- 

 ber of chance s by which the event may 

 happen, to the number by which it. may 

 both happen and fail. So that, if there 

 be constituted a fraction, of which the 

 numerator is the number of chances for 

 the events happening, and the denomi- 

 nator the number for both happening and 

 failing 1 , ihit fraction vviil properly ex- 

 press the value of the probability of the 

 event's happening. Thus, if an event 

 have 3 chances for happening, and 2 for 

 failing, the sum of which being 5, the 

 fraction 1 will fitly represent the proba- 

 bility of its happening 1 , and may be taken 

 to be the measure of it. The same 

 thing may be said of the probability of 

 failing, which will likewise be measured 

 by a fraction, whose numerator is the 

 number of chances by which it may fail, 

 and its denominator the whole number 

 of chances both for its happening and 

 Jailing : so the probability of the failing 

 of the above event, which has 2 chances 

 to fail, and 3 to happen, will be express- 

 ed or measured by the fraction .2. 



Hence, if there be added together the 

 fractions which express the probability 

 for both happening and failing, their sum 

 will always be equal to unity, or 1 ; since 

 the sum of their numerators will be 

 equal to their common denominator. And 

 since it is a certainty that an event will 

 either happen or fail, it follows that a 

 certainty, which may be considered as an 

 infinitely great degree of probability, is 

 fitly represented by unity. See CHASCES ; 

 LIFE, duration of, 



PROBATE of -trills, is the exhibiting 

 and proving wills and testaments be- 

 fore the ecclesiastical judges, delegated 

 by the bishop, who is ordinary of the 

 place where the party dies. 



By the stamp acts, a very heavy duty 

 is now payable upon these instruments, 

 and a man can entitle himself to personal 

 property only by means of a probate; 

 that is, by having proved the will. 



PROBLEM, in logic, a proposition 

 that neither appears absolutely true or 

 false ; and, consequently, may be assert- 

 ed either in the affirmative or negative. 

 A logical or dialectical problem, accord- 

 ing to the school-men, consists of two 

 parts ; a subject, about which the doubt 

 is raised ; and a predicate, or attribute, 

 which is the thing doubted, whether it be 

 true of the subject or not. Problems may 

 be divided into physical, ethical, and 

 metaphysical ; phvsical, when it is doubt- 

 ed whether such and such properties be- 



long to certain natural bodies; ethical, 

 when the doubt is, whether or not ;t be 

 proper to do or omit certain actions ; 

 and metaphysical, when the doubt re- 

 lates to spirits, &c. 



PROBLEM, in geometry, is a proposi- 

 tion wherein some operation or construc- 

 tion is required ; as, to divide a line or an- 

 gle, erect or let fall perpendiculars, he. A 

 problem is said to consist of three parts; 

 the proposition, which expresses what is 

 to be done ; the solution, wherein the 

 several steps whereby the thing required 

 is to be effected are rehearsed in order; 

 and, lastly, the demonstration, wherein is 

 shown, that by doing the several tilings 

 prescribed in the solution, the thing re- 

 quired is obtained. 



PROBLEM, in algebra, is a question or 

 proposition which requires some un- 

 known truth to be investigated, and the 

 truth of the discovery demonstrated. So 

 that a problem is to find a theoi*em. 



PROBLEM, Kepler's, in astronomy, is the 

 determining a planet's place from the 

 time ; so called from Kepler, who first 

 proposed it. It was this, to find the po- 

 sition of a right line, which passing 

 through one of the foci of an ellipsis, 

 shall cut off' an area described by its 

 motion, which shall be in any given 

 proportion to the whole area of the 

 ellipsis. 



The proposer knew no way of solving 

 the problem but by an indirect method ; 

 but Sir Isaac Newton, Dr. Keill, &c. have 

 since solved it directly and geometrically, 

 several ways 



PROBLEM, Ddiacal, or a problem for 

 finding two mean proportionals between 

 two given lines, in geometry, is the doub- 

 ling of the cube ; it was so called from 

 the people of Delos, who, upon consult- 

 ing the oracle for a remedy against a 

 plague, were answered, that the plague 

 should cease when Apollo's altar, which 

 was in form of a cube, should be doubled. 

 See CI-HE. 



PROCEDENDO, is a writ which lies 

 where a cause is removed out of an infe- 

 rior to a superior court. 



PROCELLAiilA, the petrel, in natural 

 history, a genus of birds of the order An- 

 sereS. Generic character: bill strait, 

 but hooked at the end ; nostrils generally 

 contained in one tube, at the base of the 

 bill ; legs naked a little above the knee ; 

 back toe little more than a spur. There 

 are twenty-three species, of which the 

 following are the principal. 



P. gigantea, or the giant petrel, is 

 more than three feet long, and about se- 





