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"1776.

New Criticifm on Matt. xxiii. 23.

curring any grievous penalty, as not being neceffary, and fome kinds the latter might probably cultivate in their own gardens; and with respect to their following human traditions, this can only refer to certain external ceremonies, such as washing cups and platters.

re

Third, zažia and as being both relative to the foregoing nouns, cannot with propriety be rendered by the pronoun "other;" which quires a, Tegos. The first are fometimes relatives, fometimes demonftratives, and fometimes both together as here. The laft are used in very particular fenfes ; fometimes they are indefinites they relate to, or demonftrate univerfally, without determining any one particular perfon or thing; and fometimes the contrary. But I believe neither of them are ufed as relatives in fentences fimilar to thefe, wherein the parts are properly divided and diftinguished; that is, the parts are referred to collectively, and determinate; and the intended reprehenfory conclufion adduced.

That the alteration will not obtain as intended by the author of the criticif, leveral other reafons may be urged from the laws of good speaking, and grammar. 1. For an eloquent and nice orator with us, to be guilty of fuch unneceffary tautology, would certainly admit of cenfure; much lefs fhould it be inferred that Jefus, the Chrift, who according to the teftimonies concerning him never spoke any thing in vain, nor, we may rationally fuppofe, fpoke more words than were neceffary, was guilty of what other good speakers would bluth at. 2. If only a part, and not the whole in feparate parts, were referred to, it is likely the fame pronoun would have been used, and not diverfe as here. 3. To fome acquainted with the Greek idiom, probably it may have been remarked, that in drawing conclufions from former affertions, or arguments, when the required- tenfe

201

made ufe of is derived from the fame verb, its adjective or pronoun is the relative to them; but in the part of this fentence expreffive of the things omitted, the word governing is aphare of di; and the infinitive of the fame verb is ufed in the reprehenfory part of the fentence; it may therefore be inferred from this, as likewife from the natural arrangement of the words, that the first of these pronouns relates to the firft part of the fentence, and the other, to that which is governed of the common verb. Matthew and Luke have both related this paffage, and I apprehend as tranflators, and although they have not done it exactly in the fame words, yet had we the difcourfes of Chrift in the original, and other neceffary means of knowledge, I doubt not but it would appear they defcribed the fame things. It is certain the different verbs they ufe, dpnnale, and wagixos, convey the fame idea in its place, and Matthew's Tv EO V TV TW, are equivalent to Luke's vayanÀY TỸ QEH and what Matthew calls τὸ νη θον καὶ τὸ κύκι Luke makes τὸ πήγαιον καὶ πο axavo. The former in each may be words expreffing diverfe qualities of the fame herb, for the quick growing or blooming herb may also be of an aftringent, or of fome other quality, denoted by the word to whyan, and the word λaxavov, may be a general name for an herb, plant or root of a larger genus, and which requi red to be digged out, as the others might be plucked with the hand.

According to the above obfervations the whole paffage may thus be rendered, "Woe to you Scribes and Pharifees, hypocrites, because ye have appointed tithe from the Hedyofmos, and the Anethon, and the Cumin; and ye have relinquished the weighter matters of the law, judgement and compaffion, and faith; thefe it was meet to perform, and not to relinquish thofe."

Φιλεξήγησις.

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202

On the complicated Doctrine of Tithes.

a fmall tithe." Thus in the cafe of Wallis against Underhill: a bill was exhibited in the Exchequer by the plaintiff Wallis, as tenant under the impropriator of the great tithes in the parish of Prittlewell in Kent, which infifted upon the tithe of a fecond crop of clover, which was cut and threfhed for feed, as a great tithe. Underhill, the Vicar, claimed the tithe of clover feed as a vicarial or fmall tithe. Lord chief Baron Comyns delivered the refolution of the Court; that by the canon law, as long as the diftinction hath been made between great and fmall tithes (which is as ancient as appropriations to the religious houfes who ufually engroffed the great tithes, but left the fmall tithes to the curate) all feeds have been reckoned as small tithes. The common law feems to follow the canon law in this point, and all the refolutions relating to tithes, which proceed from things newly introduced into England, have held them to be small tithes; as faffron, woad, flax, &c. All the Barons agreed in opinion that the plaintiff's bill fhould be difmiffed. Baron Parker feemed to doubt, as it partook of the nature of the ftalk, from whence it was taken. Comyns 633." "And it hath been decreed fince this cafe, that the feed of clover is a small tithe." To quote another paffage from the faid author, vol. 3. p. 394. "But if a vicar fue for tithes, and the parifhioner being a layman, denies that the faid tithes are due to him, in fuch cafe unless the vicar thall prove that the tithes in queftion are due to him by endowment, or prescription, he thall fail in his fuit: and the reafon is, becaufe all tithes de jure or in prefumption of law belong to the rector; and therefore the vicar fhall receive only

April

thofe tithes which he enjoyeth by cuftom or prescription, or by the endowment. 1. Ought. 264."

Now it appears from the firft quotation, that clover feed, and feeds in general,are in their nature small tithes. But fuppofing it has been a custom in any parifh for the impropriator to take the tithe of clover feed, and the vicar cannot prove himself entitled to the fame by his endowment, how is the vicar to have redrefs? is an ill founded cuftom to fuperfede the most exprefs and indubitable right ? furely though a vicar appears to be thus reftrained by the ftrict letter of his endowment, yet it cannot but be adjudged that he was intended to be endowed with it, because it is not included in the exception out of his endowment. Again, it has also been objected to the vicar, that though the fecond mowth of clover left for feed, may be allowed to come under the denomination of fmall tithes yet the first mowth of feed clover (or maiden feed) is certainly the rector's tithe, as being the firft feverance from the ground. But the feeds are, in their own nature, fmall tithes ; where is the difference whether they arise from a firft or a second mowth? and if the fecond mowth be allowed to be tithable by the vicar, does it not follow that from the fame principle the first mowth be vicarial tithe allo? It is not an infuperable objection that the first feverance from the ground muft neceffarily, and de jure, belong to the rector; otherwife flax would be a great tithe, which is univerfally known not to be fo. I hope fome of your correfpondents will oblige me with their opinion on the above fubject, and am, Sir, your conftant reader,

and humble Servant, VICARIUS.

To the EDITOR of the LONDON MAGAZINE.
SIR,

THE

HE illiberal attack upon the ingenious and entertaining Mr. Granger, in your February Magazine, muft not be fuffered to pals unnoticed. Does fuch a flight error as is laid to his charge, deferve fuch extravagant animadverfion? Does he not fairly eite his authority for what he fays of the excellent Bishop Bedell?" Was

not Bishop Bedell chaplain to Sir
Henry Wotton and the friend of fa-
ther Paul? And was it not highly
probable that Lilly meant to defcribe
this Bishop? But Lilly was,
doubt, mistaken in imagining that he
purchased his "choiceft books of
Aftrology" from this Bishop's li-
brary; as the dates of the Bishop's

no

death,

1776. Defence of Granger-Mathemat. Correfpondence. 203

death, and the purchase of these books, will by no means tally. However, fuppofe Lilly and Granger had been right, would it be any difrepute to the truly excellent Bishop Bedell" to have had some aftrological books in his library? If your correfpondent thinks fo, he only fhows his ignorance, As furely the famous Mr. Jofeph Mede" was not at all inferior in point of learning and virtue to Bifhop Bedell; and as "the respect then

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MATHEMATICAL CORRESPONDENCE,
Answers to the Queftions in our Magazine for February last.

[49] QUESTION I. Answered by Mr. Thomas Mofs the Propofer.

T evidently appears from the corollaries to theorems 12 and 23, pages 80

It's of appears fromm. zd. edit. that if a right line be drawn from the

angular point of any plane triangle to the middle of its oppofite fide; and from the extremes of that fide, two other right lines be drawn to interfect each other any where in the faid bifecting line, thofe lines will meet the other two fides of the triangle in two points equidiftant from that line, produced if neceffary, or which amounts to the fame, a right line joining thofe two points will be parallel to the bifected fide. This may also be demonstrated indepen-, dent of the above cited corollaries.

This being premised as a lemma; let then ABCD be P the propofed rectangle, draw the diagonals thereof interfecting each other in E. Then from the extremes of one of those diagonals (BD) to any point P without that, line, draw two right lines BP, DP; draw the line PE, 1 and through any point (m) thereof, from B and D, draw two right lines BG and DF. Then (by the lemma) the line FG, when drawn, will manifeftly be parallel to BD, and cut PEB in H. Draw BH and EF, and through the point (7) of interfection, draw PI, which (by the lemma) evidently bifects BE in I (and

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FH in K.) In like manner by drawing BK, IF, and IH, EK; and then drawing right lines from P, through the refpective points of interfection c and e, the equal parts BI and IE will also be bisected: and by the fame method each of thofe four equal parts may again be bifected, and fo on. By the very fame method of proceeding the other half ED of the diagonal may be divided into four, eight, &c. equal parts. Q. E. I. Schol. By the very fame principle (and by no other that I know of) there are alto other methods of dividing, by a pen and ruler only, the faid diagonal into 4, 8, 16, &c. equal parts. For if EF and EG be drawn, thofe lines will (by

Dd 2

204

Mathematical Correspondence.

April

(by the lemma) cut BG and DF in a and b, equidistant from BD. Hence we obtain, by a pen and ftraight ruler only, another line (befides FG) parallel to BD; by means of which parallel line, &c. BD may be divided as above: and hence it alfo appears that a line drawn through the points c and e will likewife be parallel to BD..

G

[50] QUESTION II. Anfawered by Mr. John Hampshire the Propofer. Conft. LET d equal to half the given difference of the fides, make ED equal to half the difference of the fegments of the bafe, and El a third proportional to ED and d, and having conftructed the right angled triangle CIE fo that CE may be equal to the given bifecting line, through D draw CH to meet GH (drawn parallel to CI) in H; which bifect with the perpendicular PO, meeting GH in O; with OH, as a radius, defcribe the circle HBCA to cut EI produced in A and B, join AC and BC, and ACB is the triangle required.

A

AC

F

d

K

Ο

B

F

- BC

H

Demonftration. Let AH and HB be joined, and KH and FC perpendicular to AC and GH be drawn; becaufe OP is perpendiculartu, and bifects CH, it is evident the circle paffes through C. Moreover as OE is per-. pendicular to AB, AE EB, and AH` = BH, and the angle ACH BCH, but AK = Prob. 13.) Now as the angle CDB (EDH) is to DAC + ACD = CAD + DAH, the right angled triangles AKH, EDH, and FCH, are fimilar, as well as the triangles HDB, and HCB, therefore DH: HB (HÁ) :: HB: HC, and AK: DE :: AH (HB): DH, but FC: KA :: CH: AH. Therefore FC ; KA :: KA: DE, but FC EI, by parallel lines, and EI: d::d: DE (by construction) therefore KA = d.

2

(Simplon's Trig.

Q.E. D. Mr. George Sanderfon alfo conftructed this queftion in the fame manner, and favoured us with the following algebraical folution referring to the above figure.

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=d, and AE = x, then a : 2x :: di 2dx dx + da :: x + a: = AC + CB (Eu. 3. vi.) and as 2x : ——

a

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a

(AC) = CB, but AC2 + CB2 = 2AE2 + 2C (Simp2d2x2 +2d2a2

fon's Geom B. II. Problem XI.) that is

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2b2+2x and

We were favoured wih anfwers alfo from Mr. Robins, Mr. Merrit, and others.

[51] QUESTION III. Aufwered by Mr. Bonnycaftle, mafter of the Academy at

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from A and B let be reprefented by x and y refpectively. Allo

D +B

let AC = à, ax = velocity

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BDb, and AB = c; then per question e-x : x :: a :

of P at the point N, and eyyb:
cx-xx

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fluxion of the time from A, and

1776.

Anecdote of Fidelity and Refolution.

205

fluxion of the time from B. The correct fluents of thefe fluxions, or the times themselves, found as in the answer to question III. Magazine December,

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the nature of the queftion are equal to each other; therefore by fubftituting

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found equal to 13.9 + and the time 3.7 nearly; confequently P will have travelled 13. 9 miles, and Q 6. 1.

We were fav ured with anfwers to this question by the propofer Mr. Todd, Mr. Robins, Mr. Keech, and others.

NEW MATHEMATICAL QUESTIONS.

[52] QUESTION I. By Cleonicus.

THERE is a given right line AB, divided in C, fo that AC may be greater than CB; it is required to find a mean proportional between AC and CB, with one given extent of a pair of compaffes (more or less than half the line AB) a pen and ftraight ruler only.

[53] QUESTION II. By Peletarius.

SUPPOSE a line drawn from a given point without a given circle to cut it in two points, it is required from the fame point to draw another line to cut the circumference in two other points fuch that the fum of the arcs intercepted between thefe lines may fubtend at the circumference an angle equal to a given one.

[54.] QUESTION III. By Anonymous.

THE points A and B are given, and the rectangle AC x CB is a conftant quantity, it is required to draw a tangent to the curve which is the locus of the point C, at any given point thereof.

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For the LONDON MAGAZINE.

Anecdote of Fidelity and Refolution.

W remained in Portugal, the

HILE the fhadow of freedom

greatest men in that nation were heroic and brave. A noble anecdote of this brave spirit offers itfelf. Alonzo IV. furnamed The Brave, afcended the Throne of Portugal in the vigour of his age. The pleafures of the chace engroffed all his attention. His confidents and favourites encouraged and allured him to it. His time was fpent in the forests of Cintra, while the affairs of government were neglected, or executed by thofe whofe intereft it was to keep their Sovereign in ignorance. His prefence at last being neceffary at Lisbon, he entered the council with all the impetuofity of a young fportsman, and with great familiarity

the hiftory of a whole month spent in

and gaity entertained his nobles with

hunting, in fishing and fhooting. When he had finished his narrative, a nobleman of the first rank rose up: courts and camps, faid he, were allotted for kings, not woods and defarts. Even the affairs of private men fuffer when recreation is preferred to business. But when the whims of pleasure engrofs the thoughts of a king, a whole nation is configned to ruin. We came here for other purposes than to hear the exploits of the chace, exploits which are only intelligible to grooms and falconers. If your Majefty will attend to the wants, and remove the grievances of your people, you will find them obedient fubjects.

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