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FOR THE Ingenious of Both Sexes. For

the MONTHS of January, February and March, 1734.


III. MATHEMATICAL QUESTION S. Suited both to Beginners, and also to such as have made higher Advances in those STUDIE S.

Me vero primum dulces ante omnia Muje,
Quarum facra fero ingenti perculsus Amore,

Accipiant : Cælique Vias & Sydera monfirent,
Defectus Solis varios, Lundque Labores :
Unde Tremor Terris : quâ Vi maria alta tumefcant
Objicibus ruptis, rurfusque in fe ipfa refidant :
Quid tantum Oceano properent se tingere Soles
Hyberni, vel quæ tardis mora Noétıbus obftet.

VIRGIL. Georgic.

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YORK: Printed by 'Tho. GENT, in

Coffee-rard, MDCC XXXiv.

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******* N the Year 1711, Mr. Tipper, ihe Author of,

The Ladies Diary, publisea a Book Nonibly, I

called, Delights for the Ingenious; but for Red*****

Jons by him mentioned in the Diary, 1712. he

then laid 'em aside, much Importunity has been used to beve the same re-assumed and continued ; as there. is not hing of this Nature published, but what is in the above-mention'd Diary yearly, ( except The Philosophical Transactions) and the Limits there, are so narrow, that but very litile can be inserted ; and that is oftentimes low and trifling, and sometimes implible, several of the most difficult Questions returned with only tbe bare Numbers, zout hout any algebraical Process, so that Beginners in those Studies are little instructed thereby, as if no such Thing had ever been inserted; and we may add, that Solutions absurd and erroneous are given as true. Witness those of Questions the 172, and 174 1733 as answered in 1734, especially the Prize Question, 1733, answer'd by Mr. C. Mason, by which he has demonstrated to all the World, his Ignorance in Trigonometry, and I think at the least, it argues want of Care also, in the Author, to put in de Solution, so foreign from the Truth.

The Design of the ensuing Treatise is to corre&t all this; wherein the Answers to the Questions Mall be all' at full Length ; and th ugh it be chiefly designed for the fudicus in Mathematicks, yet it will also comprehend Enigma's, Paradoxes, &c.

The Mathematick Arts need no Recommendation, they carry their own Reward with 'em, by leading us to Truth by the nearest Way, and with the greatest certainty : The Antients held them in so much efteem that their Kings were not only Encouragers of them, but Students in them, they accounting that Person unfit to govern the World who knew not what the World ws: 7 bey give us more just and adequate Notions of the Universe, and of the Situation of the Parts and extent of our ton Sistem ;

" and do molt powerfuliy demonstrate to us the Existence and Attributes


A 2

of fome Almighty designer ; 10 prove this to any Perfon, one need only to bid him consider the Sun with that iiza Sipportable Glory and Lufire that surrounds it : Tu des

monstrate the vast Distance, Mlag 11t ide, and Heat of it: To represent to him the Chorus of Planets moving perio

dicalig by uniform Laws, in their leveral Orbis about it ; aff rding a regular Variety of Aspects ; guarded some of ibin by condary Planets, and as it were einulating

the State of ihe Sun; and probably all polest by proper. Inbabitants, to remind him of those surprizing Visits the Comets makes us, the large Trains, or uncommon Spler

dor which attends them; the far Country they come from; and the Curiosity and Horror they excite, not only among us, but in the Inbabitants of other Planets, who also may

be up to see the Entry and Progress of obese Ministers of " Fate : To dire&t bis Eye and Contemplation through:

t hoje azure Fields, and vast Regions above him, up to the

fixed Stars, tbat radiant numberless Holt of Heaven ; « and to make him understand how unlikely a Thing it is, " that thev should be placed there Oirly to adorii and be

Spargle a Canopy over our Heads, and much less to supply "The Places of so many Glow-Worms, by affording a feeble

Light to our Earth, or even to all our Fellow Planets : To convince him, that they are so many other Suis, with " their several Regions and Sets of Planets about them : " To Mew bim by the Hilp of Glases, still more and more, " of obese fix'd lights, and to beger in him an Apprehension " of their unaccountable Numbers, and of the immense

Spaces, that lye retired beyond our utmost Reach, and

even Imagination : I say, one need but do this, and explain to him such things as are now known almost to every « Body, and by it to sew that if the World be not infinite, “ it is infinito Similis ; and therefore jure a mignificent 4 Structure, and the work of an infinite Architeet

Such are the Advantages we receive from the Science of Mathematicks, and as long as the Investigation of Truth continues to be pleasant (which will be always to intelligent and rarional Minds) so long will

also be above-named Study be : I Mall adjoin to rbis, the excelent Dr. Cotes's Preface to the 21. Edition of Sir Isaac Newton's Principia, as an Introducrion to the following Work, in which he news the Prebeminence of experimental Philosopby above the Hypothetical.

February the 261ho
3733-4 C.


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Extracted from Dr. R. COT E s.

HOSE who have treated of Natural
Philosophy may be nearly reduced to

thrce Clafles. Of these, fome have T attributed, to the several Species of

Things, Specific and Occult Qualities ; . on which, in a Manner unknown, they

make the Operations of the several Bodies to depènd. The Sum of the Doctrine of the Schools, derived from ARISTOTLE and the Peripatetics, is herein contained. They affirm, That the several Effects of Bodies arise from the particular Natures of those Bodies : But whence it is that Bodies de rive those Natures, they don't tell us, and therefore they tell us nothing. And being entirely employed in giving Names to Things, and not in searching into Things them selves, we may say they have invented a philosophical Way of Speaking, but not that they have made known to us true Philosophy.

OTHERS therefore, laying afide that useless Heap of Words, thought to enıploy their Pains to better Purpose. These supposed all Matter homogeneous; and that the Variety of Forms, which is seen in Bodies, arises from fome very plain and simple Affections of the component Particles : And by going on from fimple Things, to those which are more compounded, they certainly proceed right, if they attribute no other Properties to those pri


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