Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	king_n	write_v	year_n	5,160	5	4.8919	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A42822	Plus ultra, or, The progress and advancement of knowledge since the days of Aristotle in an account of some of the most remarkable late improvements of practical, useful learning, to encourage philosophical endeavours : occasioned by a conference with one of the notional way / by Jos. Glanvill.	Glanvill, Joseph, 1636-1680.	1668 (1668)	Wing G820; ESTC R14223	65,458	192

futilities of that National way But not to take too large a compass this is certain That Geometry is a most useful and proper help in the affairs of Philophy and Life 'T is almost as clear from those former intimations that Aristotle was not much enclined that way and we know that his late Sectators have very seldome applied themselves to Geometrical Disquisitions The Result of which is We must expect the Advantages of this Science from the declining of his and their Empire and I need not say expect it they are both in present view And if after this you require accounts of the Improvements Geometry hath received since the foundation of that Tyranny by the Man of STAGYRA I shall offer you the best I have and though I am conscious that they will be scant and defective yet I hope sufficient for my present purpose I note then from the celebrated Vossius That Euclide was the first that brought Geometry into a Method and more accurately demonstrated those Principles which before were scattered among the Greeks and Aegyptians and not so cogently or carefully proved And Proclus reckons this Famous man as the Compiler and Demonstrator not as the Inventor of the Elements and two of these Books viz. 14. 15. are ascribed to Apollonius Pergaeus who was his nearest Successor in Fame for Mathematical Abilities This Geometrician improved the Science by four Books of Conicks publish'd of old and three more have been lately in the year 1661. translated out of an Arabick Manuscript in the Duke of Tuscany's Library and are now abroad This Manuscript Iacob Golius procured out of the East Besides which this Magnus Geometra as he was called illustrated Euclide by his Learned Commentary upon him But Archimedes of Syracuse was a Person of the greatest renown for Geometrical and Mechanical Performances concerning which Polybius Valerius Plutarch Livy and others have recorded prodigious things This great Wit carried Geometry from general and idle Speculation to the use and benefit of Mankind whereas before him it was an ancient and perverse Opinion That this Knowledge ought not to be brought down to vulgar Service but kept up in abstractive Contemplations upon which score Archytas and Eudoxus those great Geometricians before Euclide were scared from the Mechanical and Organical Methods to the great hindrance of beneficial Improvements in that way But the excellent Syracusian understood that this Science is not debased but promoted and advanced by such Accommodations and evinc'd the usefulness and excellency of Geometry in his admirable Paradox proposed before King Hieron Datis viribus datum pondus tollere 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 This Mathematician flourish'd 160 years after the time of Aristotle who hath the name of the most ancient that writ in Mechanicks though that Book of his be not mentioned either by Archimedes Athenaeus Hero or Pappus Mechanical Authors and Cardan and Patricius affirm that Work to be none of Aristotle's Whos 's ever it was the Performance hath praise from the Learned as explaining the general Causes of Mechanical Geometry But Archimedes was more practical and particular And though Plutarch in the Life of Marcellus affirms he writ nothing yet the contrary is abundantly proved by Gerard Vossius who hath shewn that the Books extant under his Name that contain so many great Maxims of Mechanicks are genuine and both Strabo and Pappus mention them as his The Design of Archimedes of combining Mechanism and Geometrick Theory was after happily promoted by Hero the Elder of Alexandria who invented those ingenuous Automata that move by Air and Wyres concerning which he writ a Book that was Translated by Fredericus Commandinus as also he did another De Machinis Bellicis by which he well improved Geometrick Mechanicks And Pappus particularly celebrates his exactness in solving the Deliaick Problem De Cubo duplicando acknowledging that he took most of his own Accounts about that matter from that exquisite Man Next him I mention Theodosius of Tripoli who very much improved Geometry by his three Books De Figur a Sphaerica which afforded great assistance to Ptolomy Pappus Proclus and Theon in their Mathematical Endeavours Menelaus also who lived in Trajan's time contributed very much to the perfecting the Doctrine of Sphaericks as Vitellio well knew who was famous for those things which he borrowed from that Author The Performances also of Ctesibius who lived in the time of Ptolomaeus Physcon are much celebrated by Pliny He invented many things in Hydraulicks and according to Athenaeus he was the first Contriver of Musical Organs These were Mechanical but Geminus Rhodius the Master of Proclus Lycius applied Logick to Geometry out of particular Elements abstracting Vniversals He demonstrated That there are only Three similar Species of all Lines viz. Right Circular and Cylindrical And Perseus following his steps enrich'd Geometry with the Invention of three kinds of Crooked Lines the Parabole Hyperbole and Elipsis for which he express'd his extatick joy as Thales Pythagoras and Archimedes did upon like occasions in a Sacrifice to the Gods But to be briefer Pappus improved the Sphoericks Theon more methodically digested the Elements of Euclide Serenus Antinsensis discover'd that the Section of a right Cylindre is the same with the Elipsis of a right Cone Copernicus improved the Doctrine of Triangles Ramus corrected and supplied Euclide where his Principles were defective Maurolicus writ first of Secant Lines Clavius much illustrated and promoted the Doctrine of Tangents Secants Triangles Right Lines and Sphaericks besides what he did in his Comment upon Euclide I might mention with These the worthy Performances of Cusanus Pitiscus Snellius Ambrosius Rhodius Kepler Franciscus à Schoten and others who contributed very eminently to the perfections and advancements of Geometry and were late men But none have done in it like the excellent Persons whom I reserve for my last mention The chief are Vieta Des Cartes and Dr. Wallis CHAP. IV. Improvements in Geometry by Des Cartes Vieta and Dr. Wallis IN order to my giving an account of some of their Performances I must premise That no great things can be done in Geometry without the Analytical Method And though some Learned Men conceive the Ancients were acquainted with this way of resolving Problems yet their skill in it went no higher than the Quadratick Order of Aequations which They demonstrated by Circles and Right Lines which They call'd Loca plana but they were able to do nothing in the Cubical Aequations or any of the Superiour Orders though they endeavour'd to cover their defects in this Art by recourse ad Locos Solidos viz. Conick Sections and Lineares as they called them such as the Helix Conchoeides and those of like nature But those tortous and curved Lines being described Mechanically by Compound Motions the Problems resolv'd by them are performed Organically by the hand and eye not Geometrically This was the State of the Analytick Art as long as Learning flourish'd in Greece when That was subdued