PRO 



PRO 



a c 



b d 



If the terms of an harmonic proportion 

 be continued, then it is called an harmon- 

 ic progression. Thus, supposing 

 CA, to be the 2d term, 7 



\d, the difference of the 1st and 2d, 5 

 and that the 1st exceeds the 2d. The 

 progression will be 



-f A d A* + A il A+ A d 



A + 4 <*' 



"*" , &c. Whence, if out of a rank 

 A j~ 5 u 



of harmonic proportionals, there be taken 

 any series of equidistant terms, that se- 

 ries will be harmonically proportional. 

 And this kind of proportion has several 

 other properties common with arithmetic 

 .and geometric proportions. 



When three terms are so disposed, that 

 the difference of the 1st and 2d : differ- 

 ence of the 2d and 3d : : 3d : 1st, they are 

 said to be in a contra-harmonic propor- 

 tion. Thus, 6, 5, 3, and 12, 10, 4, are 

 contra-harmonics. For 6 5:5 3 : : 

 3 : 6; and 12 10 : 10 4 : : 4 : 12. 

 Or, supposing A greater than ?z, if the 2d 

 term be greater than the 1st : 



Then A n + n z , h 1 + n 2 , A 1 + A n, are 

 contra-harmonics, for h n A a : n hn 

 : : A* + A n : h n + n. 



But if the 1st term exceeds the 2d, then 

 A 1 + A n, A 1 -h w 2 , A n -f- n 2 , are contra- 

 harmonics. For A n- n 1 : A 1 An:: 

 A n -f w 1 : A 1 + A n. 



PROPOSITION, in logic, part of an ar- 



gument wherein some quality, either ne- 



gative or positive, is attributed to a sub- 



ject, as " God is just." While the com- 



paring. of our ideas is considered merely 



as the act of the mind, assembling them 



together, and joining or disjoining them 



according to the result of its perceptions, 



this operation is called judgment. But 



when these judgments are expressed in 



words, they then bear the name of propo- 



sitions. Hence a proposition is a sen- 



tence expressing some judgment of the 



mind, whereby two or more ideas are 



affirmed to agree or disagree : and as our 



judgments include at least two ideas, one 



of which is affirmed or denied of the 



other ; so a proposition must have terms 



corresponding to these ideas. The idea 



of which we affirm or deny, and of course 



the term expressing that idea, is culled 



the subject of the proposition ; and the 



idea affirmed or denied, as also the term 



answering to it, is called its predicate ; 



thus in the proposition, God is omnipo- 



tent, God is the subject, it being of him 



that we affirm omnipotence : and omnipo- 

 tent is the predicate, because we affirm 

 the idea expressed by that word to be- 

 long to God. 



PROPOSITION, in mathematics, is ei- 

 ther some truth advanced, and shown to 

 be such by. demonstration, or some opera- 

 tion proposed and its solution shown. If 

 the proposition be deduced from several 

 theoretical definitions compared together, 

 it is called a theorem ; if from a praxis, 

 or series of operations, it is called a pro- 

 blem. 



PROPOSITION, in poetry, the first part 

 of a poem wherein the author proposes 

 briefly, and in general, what he is to say 

 in the body of his work. It should com- 

 prehend only the maiter of the poem, 

 that is the action and the persons that act. 

 Horace prescribes modesty and simplici- 

 ty in the proposition, and would not have 

 the poet promise too much, nor raise in 

 the reader too great ideas of what he is 

 going to relate. 



PROSERPINACA, in botany, a genus 

 of the Triandria Trigynia class and order. 

 Natural order of Inundatse. Hydrocha- 

 rides, Jussieu. Essential character: ca- 



s three parted, superior : corolla none; 

 upe with a three celled nut. There is 

 but one species, viz. P. palustris, a native 

 of Virginia in marshes. 



PROSODY, that part of grammar which 

 treats of tht quantities and accents of 

 syllables, and the manner of making verses. ( 

 The English prosody turns chiefly on two 

 things, numbers and rhyme. 



PROSONOMASIA, a figure in rheto- 

 ric, whereby allusion is made to the like- 

 ness of a sound in several names or 

 words. 



PROSOPIS, in botany, a genus of the 

 Decandria Monogynia class and order. 

 Natural order of Lomentace?e. Legumi. 

 nosae, Jussieu. Essential character : calyx 

 bell -shaped, five-toothed ; stigma simple ; 

 legume linear, many-seeded. There is 

 but one species, viz. P. spicigera; it is 

 a native of most parts of the Coromandel 

 coast, flowering during the cold season ; 

 the pod of this tree is the only part used ; 

 it is nearly an inch in circumference, and 

 from six to twelve inches long; when 

 ripe, it is brown aiid smooth, containing 

 besides the seeds, a large quantity of a 

 brown mealy substance, which the natives 

 eat ; it has a sweetish agreeable taste. 



PROSOPOPOEIA, a figure in rhetoric, 

 whereby we raise qualities, or things in- 

 animate, into persons. This figure is di- 

 vided into two parts : 1. when good and 

 bad qualities, accidents, and x tbing$ in- 



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