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Verb Active, Indicative Mode, Past Time, third Person Sing, agreeing with the Nominative Case John; saying, Present Participle of the Verb Active to say, joined to the Substantive John; unto (b.) them, a Pronoun, third Person, Plural, Objective Case, governed by the Preposition unto; all, (b.); I, Pronoun, first Person Singular; indeed, an Adverb; baptize, a Verb Active, Indicative Mode, Present Time, first Person Singular, agreeing with the Nominative Case I; you, Pronoun, second Person Plural, Objective Case, following the Verb Active baptize, and governed by it; with, a Prep.; water, Subst. Objective Case, governed by the Preposition with; but, a Disjunctive Conjunction: one, a Pronoun, standing for some person not mentioned by name; mightier, an Adjective in the Comparative Degree, from the Positive mighty; than, a Conjunction, used after a Comparative word; I, (b.) the Verb am being understood; that is than I am; cometh, a Verb Neuter, Indicative Mode, Present Time, third Person Sing. agreeing with the Nominative Case one; the latchet, Subst. of, (b.) whose, Pronoun Relative, one being the Antecedent to it, in the Possessive Case; shoes, Subst. Plural, Objective Case, governed by the Preposition of; I (b.) am Indicative Mode, Present Time, first Person Sing, of the Verb to be, agreeing with the Nominative Case I; not (b.) worthy an Adjective; to unloosé, a Verb Active in the Infinite Mode, governing the Substantive latchet, in the Ob jective Case; he, (b.) shall baptizé, a Verb Active, Indicative Mode, Future Time, made by the Auxiliary shall, third Person Sing. agreeing with the Nominative Case he; you, (b) with the (b.) Holy, an Adjective; Ghost, a Subst. and with (b.) fire, a Substantive: this and the former both in the Objective Case governed by the Prep. with...

6. Now an Adverb; when a Conjunction; all, (b.) the people, a Subst. were baptized, a Verb Passive, made of the Auxiliary Verb to be, joined with the Participle Passive of the Verb to baptize, Indicative Mode, Past Time, third

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Person

Person Plural, agreeing with the Nominative Case Singular, people being a Noun of Multitude; it, Pronoun, third Person Singular, Neuter Gender, of the Nominative Case ; came (b.) to pass, Verb Neuter, Infinite Mode; that, a Conjunction; Jesus, a proper Name; also, an Adverb; being, Present Participle of the Verb to be; baptized, Participle Passive of the Verb to baptize; and (b.) praying, Present Participle of the Verb Neuter to pray; Jesus being baptized and praying is the Case Absolute, as before; the heaven, Substantive; was opened, Verb Passive, Indicative Mode, Past Time, third Person Singular, agreeing with the Nominative Case heaven, the Auxiliary Verb to be being joined to the Participle Passive, as before; and the holy Ghost, (b.) descended, Verb Neuter, Indicative Mode, Past Time, third Person Singular, agreeing with the Nominative Case Ghost; in a (b.) bodily, an Adjective; shape, a Substantive, Objective Case, governed by the Preposition in; like, an Adjective; a dove, Substantive, Objective Case, the Preposition to being understood, that is, like to a dove; upon, Preposition; him, Pronoun, third Person Singular, Objective Case, governed by the Preposition upon; and, (b.) lo, an Interjection; a voice, Substantive, Nominative Case, there was being understood; that is, there was a voice; from, Preposition; heaven, Substantive, Objective Case, (b.) saying, (b.) this a Pronominal Adjective, person being understood; is, Indicative Mode, Present Time, of the Verb, to be, third Person Singular, agreeing with the Nominative Case this ; my, a Pronominal Adjective; beloved, an Adjective; Son, a Substantive, Nominative Case, after the Verb is; in, (b.) whom, Pronoun Relative, Objective Case, governed by the Preposition in, the Substantive Son being its Antecedent; I am, (b.) well, an Adverb; pleased, the Passive Participle of the Verb to please, making with the Auxiliary Verb am a Passive Verb, in the Indicative Mode, Present time, first Person Singular, agreeing with the Nominative Case I.

CHAP.

THE

MODERN PRECEPTOR

CHAPTER, II.

ON ARITHMETIC.

W. HATEVER is in its nature capable of augmentation and diminution, is termed quantity: extent, duration, weight, &c., are all quantities: and whatever constitutes quantity, becomes an object of mathematical investigation. That branch of mathematics which considers quantity, as expressed by numbers, is called Arithmetic, from a Greek term signifying number; and may hence be considered as the science of the nature and properties of numbers: its object is to discover sure and easy methods of representing, compounding, and decompounding numbers; by certain operations, constituting calculation.

As all calculation is founded on a knowledge of what is called Unity, it must be observed, that an Unit is a quantity assumed at pleasure, to serve as the medium or standard of comparison, between quantities of the same sort. Thus, when we affirm of two bodies, that the one weighs three pounds, and the other five pounds, we make a pound the standard of comparison, or the Unit: but if we say that the first body weighs forty-eight ounces, and the other eighty ounces, we consider the ounce to be the standard or unit.

By numbers we express how many units, or parts of an

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unit, are contained in any given quantity. If the quantity consists of entire units, the number by which it is expresed, is called a whole number, as for example, sixteen, fiftynine, two-hundred and four, &c.: but if the quantity contain only parts of any given unit, as three quarters of a pound, the number is called a fraction; and when the quantity consists of entire units and parts of an unit, the number expressing it is said to be fractional, as nineteen and nine-tenths.

Arithmetic must have been known from the earliest period of society: but, although, we cannot conceive a nation, nor even a rational individual to have subsisted without a knowledge of numbers, in their most simple application and uses, yet men may have continued for many ages ignorant of the wonderful extent of their powers. The Greeks were the first European nation who cultivated the art of numbers; and some have imagined, from the terms employed by them, and by the Romans after them, that in their Arithmetical operations, they made use of small stones or pebbles: for both the Greek term Psephizo, and the Latin Calculo, (from which we have our Calculation), are derived from the words in those languages, signifying a pebble, or small stone.

However this may have been, we find the Greeks very early making use of the letters of their alphabet, to represent numbers. Thus the twenty-four letters taken as they stand in the alphabet, with three other characters, introduced in certain places, were made to represent the nine digits, the nine tens, and the nine hundreds.

But the difficulty of carrying on arithmetical operations, to much extent, with such characters, may be easily imagined, and is very evident from calculations still remaining in the works of some ancient Greek geometricians.

The Romans who drew from the Greeks the chief part of their skill in the Sciences; imitated them also in this mode

of

of expressing numbers; but adopting a different arrangement of the alphabetical characters, as here shown,

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One, Five, Ten, Fifty, One Hundred, Five Hundred,

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By the repetition and combination of these numeral characters, any number may be expressed. 1st. By the repeti tion of a character, the value is also repeated, as, III. represent three; XX. twenty; CC. two hundred,

2d. When a character is followed by one of inferior va lue, their values are to be added together, as XII. twelve, LV. fifty five. MDCCCVIII. one thousand eight hundred and eight.

3d. But when a numeral letter of small value is placed before one of a greater, the less is to be subtracted from the greater, in order to have the value of the expression: thus IV. represent four, IX. nine, XL. forty, XC. ninety. CD. four hundred, &c.

In old Books we meet with 10. instead of D. for 500. and CIO for 1000, but these characters may perhaps have been only inaccurate representations of D and M.

Thousands are also represented by drawing a short line over the numeral character as V. for 5,000. L. for 50,000. CCC. for 300,000.

About the end of the 2d century, a new species of arithmetic was invented, as is supposed, by the great geometrician and geographer Ptolomy. Its object was to avoid the difficulties occasioned by fractions in the common Arithmetic and in it the unit was divided into 60 equal parts; each of these into 60 others; each of these last again into 60 other parts, and so on: and from these divisions this kind of Arithmetic was called Sexagesimal, or by Sixties. The excellent mode of expressing Numbers now used, came into Europe from the Arabians, by way of Spain:

but

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