Paraphrafe to the last Year's Latin, in plain English. CHAMPIONS for Liberty as well as Truth (defying Pope and Pretenders) are bound by their Fidelity to oppofe whatever appears defigned to difcolour Truth, and fubvert Loyalty. II. Quære 22. answer'd by Mr. Rowland Oliver. 1. Pride and Vanity are the Caufes, why Men fet up for Critics without Judgment. "Of all the Caufes which confpire to blind POPE. By Pride and Vanity the Servant, in Opinion, equals or exceeds his Mafter. As by the Help of those two Qualities the Taylor criticises SHAKESPEAR'S Plays; the Plowman the PARSON's Sermon, and also the Bible; and Tinkers and Coblers every Day mend the Government. 2. Proftitution of Principle and Reafon, to a Party, is for SelfIntereft, or private Advantage, for which some find their public Reward. 3. Want of Probity is the Caufe when a Steward (public or private) betrays his Truft. III. Quære 23. answer'd by 'Squire Foxchace. Whether the Money yearly spent in Law-Suits equals the Property in Dispute or not, it evidently amounts to too exceffive a Sum. VII. Quare 27. anfwer'd by Mr. Potter, of Duke-fireet, To the Author of the Ladies Diary. SIR, Your bumble Servant means nothing. VIII. Quare 28. anfwer'd by Mirificus. John Potters Compliments have ever been allow'd as Marks of Manners and Refpect, as they are Incitements to Benevolence and Friendship: but fawning Flattery, or the Appearance of it, is Abfurdity, and hateful to Perfons of true Senfe and Honour. And who but the Abfurd would fuppofe Compliment to be mean Flattery, or Proftitution of Sense? Wife and virtuous Men are animated, but never captivated with Applaufe; and weak or bad Minds are encourag'd to mend their Faults by its ironical Application. IX. Quare 29. anfwer'd by XgovovcovorπÚČNO. Modefty is a Principle of Virtue, whence Shame arifes, or any Consciousnefs of deferv'd Reproach; and where there is no Shame there can be no Virtue; and the contrary is also true, where there is no Virtue, or Confcioufnefs of deferv'd Honcur, there can be no Shame. MODESTY MODESTY is represented by the Painters as a Virgin cloth'd in Bluei and SHAME as a Bawd, expos'd naked. X. Quære 30. anfwer'd by Honeftus Publicus. Morals are the Productions of the Principles of Virtue, and Reafon ; being the Fruit of an honeft Mind. Manners are the Marks of Refpect; but not always what they pretend. Morals make us true Friends, but Manners, à la Mode, often make us Diffemblers, Hypocrites, and Idolaters, to one another. Drefs up a Clown in the Form of a Pageant of Power and Intereft, and the Idolaters will foon fall down and worship. True Worth (confifting in benevolent, friendly, and generous Principles) is a Jewel feldom to be met with. The Ignorant and Vulgar (captivated by Show, and the Pomp of Equipage, paying their fuperftitious Homage to Intereft in Prospect, and Delufion in Event) are fit Tools of Power and Popery; by adoring the Shrines of Men with much more Zeal than they worship their MAKER. Hats (which are the Signals of Manners and Refpect, when put in Motion, and which the Quaker is fparing to display) promote the Trade and Commerce of this Nation, in their wearing out; as by their different Forms and use, the modest and moral Man is diftinguished from the impudent Coxcomb and abandon'd Rake! To the latter Part of the Quare. Kindnefs confifts in true Friendship, Complaifance in friendly Pretenfion. Honour is known by true Worth, Oftentation by what affects it. Dignity differs from Affectation as effentially as Wisdom from Folly; and Friendship from Self-love, as Generofity from Meannefs of Spirit. Animadverfion. Falfe Honour and falfe Homage are often affumed and paid by Men in their feveral Stations, while true Honour and Efteem belong only to the Worthy. Some exact Ceremony from Station, Office, or Appearance, who, lifting themselves in Opinion, never confider that Efteem, which is the only true Homage, must be won, and cannot be extorted. Acquaintance and Friendships being generally Confederacies in Vice and Folly, there is no Part of Education requires more to be cultivated than that of Rules for choofing Acquaintance, and fixing Friends. For, while Benevolence is due to All, each would avoid Hurt from Particulars, the certain Confequence of Affociation with unprofitable or ill Acquaintance; whether the Litigious, Vain, Affected, Idle, Imperious, Impertinent, Lewd, Abandon'd, Expenfive, Gaming, Sottish, Mercenary, or any other of the worthless kind. And as Obligations are the Traps with which the Defigning often catch the Unwary, either to repay them with Servility, or double and treble Advantages, they fhould carefully be avoided by the Prudent; as the Acceptance of Obligations (except from Superiors, or Perfons of known Honour, or Probity) is attended with many Difadvantages. Men of Learning, and Genius, without Morals and Gratitude, ought to be detefted! while the plain honeft Man of Integrity is eligible for his VIRTUE! by which Nobility itself, and every human Accomplishment receives its Worth, or is dignified and enhanc'd. Honeftus Publicus ANSWERS to the QUESTIONS in laft Year's DIARY. I. QUESTION 347 anfwered by Mr. Terey, of Portsmouth. L ET ABC be the A; then on the Bafe A B (per 33. *. 3.) defcribe two Segments of a Circle, ACB and A HB, containing the given <s; thro' the Centers D, E draw DG; allo draw DH, EC to the CK; and let fall CG and HF1s to GD. By Trigonometry, AD DH: = 17,0104α; AE=EC= 20,7531b; ID=,593651 = c; IE 11,9035=d: Put x=CK, then (by 47. e. 1.) a a - c c — ċ x — — x x = - d d + 2 d x x x = CG=HF; hence x=2c4d + − a xb+a, +2c+d2 3 KI 2,2524; AC I bb 32,5340CK; whence 35,7204; CB37,8036; and the Area 3A. IR. 33,078 P. required. Mr. Widd's Solution agrees. Mr. F. Holden folves it by the fame Method, and brings out the fame correct Numbers; with which Mr. T. Cooper's Solution, by another Method, exactly agrees. Philotbeoros folved it. The fame anfwered by Nichol Dixon, of Blackwel: Put Tangent A C B 50°, and T= Tangent < ADB 920, and 2 b AB 34 Poles, y DE DC, EF, the Distance from the CE to the Middle of the Bafe. Then, by Trigonometry, as y: I :: Tangent<ED B ; and b X b -x: A Tangent <ADE: Now, by Prob. 8. P. 21. of Mr. Emerfon's excellent Trigonometry, As I -. T; and, by the fame Reasoning, t; from which Equations y 4 b b: But Rad. divided by the Tangent Co-tangent : Mr. Jofeph Orchard, of Gefport, putting b and x as above, Tang. v, Tang. <ACBt, Rad. I, makes <ADB = 92° the Tangents of the respective <s 4 by 2 by and t, the Equations brought out of Fractions, bb + xx the former multiplied by t and the latter by ; and, taking the Sum t of both; we get 2 v + x2b=3&ty, whence =2v++ x 2 b vt X 3 16.2665, whence the Area as before. Mr. Bevil folves it by the fame Method, whofe Numbers exactly agree: As do the Solutions of Mr. Stephen Hartley, Mr. Cottam at his Grace the Duke of Norfolk's, Mr. Charles Smith, Mr. Richard Gibbons, Mr. John Wigglefworth, Mr. John Cross, and fome others. II. QUESTION 348 anfwered by Mr. J. Orchard, WritingMafter and Teacher of the Mathematics, at Gofport. ET GC = 30 Inches, AE L2635 Inches, m =,7854, and KC x. Then K Gα- x; and per Sem. Ls GCA, GKP, a;b:: P H 8 mbb xax-xx Then 3 a Solidity of the Spheroid, which, or ax-xx, is a Maximum. In Fluxions a a x — 4xx=o, whence x=1⁄2。. Again, Let GL=LI=x; per Sem. As GAC and is the Conoid's Solidity, which, or a ax-za xxx 3, is a Maximum. In Fluxions a ax- -4axx+3x 2 x10 whence Thefe Values of x fubftituted in the Maximums, and Dimenfions, by proper Theorems for the Segments and Fruftums, the Content of each Solid, with the Ratio they are in, are exhibited in the following Table, by Mr. Joseph Orchard, Generating Philotbeoros folved it. Mr. Terey's Solution: =35, CG a=30, and -2,78539, &c. Solidity=bbax S9621,0274. 1. Then put CK=x: As a:b:: a-x: but PQXAE = Diam. Spheroid; whence its Content a 2 x x = 0, and xa, by writing which Value in the above Expreffion, its Content: I 2 of SContent of the Conc. 2. To find CI? (N is the Center of the Spheroid) NG: NK ::NK: NI; i. e. 4 a: 4a :: NI. Whence CI 1 I 3 I I = 4, IK: a. By Fluxions; Content of the spheroidal Segment =3 T for x,; then the Segment HK F = of 5. 4. To find the greatest parab. Conoid BLD? Let LC=x, then" 2ab-2bx HF, a BD2; whence the Content BLD= xx, a Max. from whence, by Fluxions, *=*=CL, and L Ga; confequently, the Contact, in this Cafe, cuts off of the Axis, viz. IC, the fame as of the Spheroid: For x put, and the Conoid BHLFD: |