LESSONS IN ALGEBRA. 



315 



CONJUGATION OF THE VERB PKXTIRSI, to repent. 

 Tho conjugation of this verb is an example of the combination 

 of tho reciprocal or conjunctive pronouns mi, ti, ei, vi, and ri 

 with a verb. 



I. INFINITIVE MOOD. 1 



Preeent. Part Participle. 



Pontini, to repent. Pentitoii. pcntltaii. pentftUi, 



I'l-SiM.:.,!, ';' '' ' 



Per/erf. 

 tssnrsl pentito, to have repented. 



Future. 



per peutiriii, to be about to 

 repent. 



Promt Partidpl*. 



Preeent Germd. 

 Pcnteudoai, repenting. 



PenWntesi, repenting. 



Poet Gerund. 

 EMendosl pontito, having repented- 



Future Gerund. 



Ewi-ndo per pentirti, being about 



to repent. 



II. INDICATIVE MOOD. 



Sin-j. Io mi pinto, I repent. 



Tu ti 



EgU si pt-uto. 

 Ptur. NVi ri |'iititiiuo. 

 Voi vi peutito. 

 Egliuo si poutono. 



Imperfect. 

 Sing. Io mi peutiva, I repented. 



Tu ti pontivi. 



Egli si pontira. 

 Plur. Noi ci pentivatno. 



Voi vi peutivato. 



Eglino si peutivono. 



Indeterminate Preterite. 

 Sing. Io mi pentii, I repented. 



Tu ti peutisti. 



Egli si pcuti. 

 Plur. Noi ci peutimmo. 



Yoi vi peutiste. 



Eglino si peutirono. 



Determinate Preterite. 

 Sing. Io mi sono pentito, I have 



Tu ti sei pentito. [repented. 



Egli si c pentito. 

 Plur. Noi ci siamo pentiti. 



Voi vi sieto pentiti. 



Egliuo si sono peutiti. 



Indeterminate Pluperfect. 

 Sing. Io mi era peutito, 7 Had 

 repented. 



Tu ti eri pentito. 



Egli si era pentito. 

 Plur. Noi ci eravamo pentiti. 



Voi vi eravate pentiti. 



Egliuo si erauo peutiti. 



Determinate Pluperfect. 

 Sing. Io mi fui pentito. I had re- 



Tu ti fosti pentito. [peuted. 



Egli ii fu peutito. 

 Plur. Noi ci fummo pentiti. 



Voi vi foste peutiti. 



Eglino si furono peutiti. 



Puture. 

 Siny. Io mi pentiro, I hall repent. 



Tu ti pentir:ii. 



Egli si pentira. 

 Plur. Noi ci j.t-nt iivmo. 



Voi vi peutirete. 



Eglino si pentiranno. 



Future Perfect. 

 Sing. Io mi saro pentito, I shall 



have repented. 

 Tu ti sarai pentito. 

 Egli si sara pentito. 

 Plur. Noi ci sardmo pentiti. 

 Voi vi sare'te pentiti. 

 Eglino si saranno pentiti. 



Conditional Present. 

 Sing, lomi pentirei, I should repent. 



Tu ti pentiresti. 



Egli si pentirdbbe. 

 Plitr. Noi ci pentirt'mmo. 



Voi vi pentirdste. 



Eglino si pentirebbero. 



Conditional Paet. 

 Sing. Io mi sarei pentito, I 7iould 



have repented. 

 Tu ti sarcteti pentito. 

 Egli si sari'bbe pentito. 

 Plur. Noi ci sarcmmo peutiti. 

 Voi vi sardste peutiti. 

 Egliuo si sarobbero pentiti. 



III. IMPERATIVE MOOD. 

 Sing. Pentiti tu, repent thou. 



Non ti pentire, do not thou repent. 



Pcntasi egli, or si penta egli. 

 Plur. Pentiamoci noi. 



Pentitevi voi. 



Puutausi eglino, or si pentono eglino. 



IV. SUBJUNCTIVE 

 Present. 



Sing. Io mi penta, I may repent. Sing. 

 Tu ti poiita. 

 Egli si pcnto. 



Plur. Noi ci pentiamo. Plur. 



Voi vi pentiite. 

 Eglino si peutano. 



Imperfect. 

 Sing. Io mi pentlssi, Z might Sing. 



repent. 



Tu ti pentissi. 

 Egli si pentisse. 



PZur. Noi ci pentissimo. Plur, 



Voi vi pentiste. 

 Eglino si pentissero. 



MOOD. 



Perfect. 



Io mi sia pentito, I may have 

 Tu ti sia pentito. [repented. 

 Egli si sia peutito. 

 Noi ci siamo pentiti. 

 Voi vi siate pontiti. 

 Eglino si siano pentiti. 



Pluperfect. 

 Io mi fdssi pentito, I might 



have repented. 

 Tu ti fossi pentito. 

 Egli si fossi pentito. 

 Noi ci fossimo pentiti. 

 Voi vi foste pentiti. 

 Eglino si fossero pentiti. 



I. RBKAJUU ox THE Ivnvrrnm MOOD. 



ObMrre, the pronoun *i only refeni to the third pcrton. tinyular 

 (', e.g., in the sentence in-ye-yndn-da-ri t-<jl\ in m6l-te 

 rtO'iM-re di ri-a-equ\-tt'Lre an-aj-ra, la tu-a, a.it-<rf-na, a* 

 he endeavoured in many way* to regain agmin thy friendship, 

 the gerond ingeynandori evidently refen to the pronoun egli of 

 the third person singular ; while in the seoteooe, dl-U dtn~nt 

 pfa-errtta dv-par-tfr-ri <lH-la vil-la, it pleased the ladies to go 

 away from tho rilla, the infinitive dipartirii refers to dcmiu, 

 i.e., to the third person plural. A complete conjugation, for 

 example, of the present and past gerund*, being in all person* 

 of frequent use, runs as follows : 



Preeent Gerund. 

 Sing. Pentndomi, at I repent. 



Pont^ndoti. 



Pentt-u'loi. 

 Plur. Pentiudoci. 



Pentc'-U'lovi. 



iVut, -II.IOHI. 



P<ut Gerund. 



tf. Esstodomi pentito, <u / 

 EsstodoU peotito. 

 Eettodori peutito. 



-^a.,4 ' *1 



, t 



;...:. t.ti. 



LESSONS IN ALGEBRA. XXXIL 



EEDUCTION OF EQUATIONS BY EVOLUTION. 

 IN many equation* tho letter which expresses the unknown 

 quantity is involved to some power. Thus, 

 in the equation z* = 16, 

 we have the value of the square of z, but not of z itself. 



If the square root oi both sidoa be extracted, 

 we shall have tt 4. 



The equality of the members is not affected by this reduction. 

 For if two quantities or sets of quantities are equal, their roots 

 are also equal. 



If (x + a) n = b + h, then * -f a = n / b+ h. Hence, 



To reduce an equation when the unknown quantity is a 

 power, 



Extract the root of both tides which correspond* with th* 

 power expressed by tlie index of the unknown quantity. 



EXAMPLES. 



1. Eeduce the equation 6 + z 2 - 8 = 7. 

 By transposition, ,z 2 = 7 + 8-6 = 9. 



By evolution, * = ^9 = + 3. Ant. 



The signs -f and are both placed before V9, because an 

 even root of an affirmative quantity is ambiguous. 



2. Eeduce the equation &r 5 30 = z 1 + 34. 

 Transposing, etc., at 2 = 16. 



By evolution, = 4. Aii*. 



From the preceding articles it will be easy to see, that to 

 reduce an equation containing a root of a power, requires both 

 involution and evolution. 



EXAMPLE. 



Eednce the equation V* 2 = 4. 

 By involution, z 3 = 4 s = 64. 



By evolution, * = + 



EXEECISE 60. 



1. Reduce the equation ajfl 5c = kr* So + d. 



2. Reduce the equation a + di* = 10 - z*. 



o = h - d, 



= _ 8. Ant. 



3. Reduce the equation V-f 



4. Reduce the equation (* + a)' 



5. Reduce the equation (*' - 1)* = 



6. Reduce the equation -/x 1 11 = 



7. Reduce the equation J\p 4ob : 



_ 

 + J& + ** 



(*- D* 

 5. 

 a b. 



6. Reduce the equation (13 + v^S + 



9. Reduce the equation (3 + J9& + **; *** 



PBOBLEMS. 



1. A gentleman being asked his age, replied, " If yon add to 

 it 10 years, and extract the square root of the sum, and from 

 this root subtract 2, the remainder will be 6." 

 age? 



What WM his 



