Elements of philosophy, the first section, concerning body / Written in Latine by Thomas Hobbes of Malmesbury. And now translated into English. To which are added six lessons to the Professors of Mathematicks of the institution of Sr. Henry Savile, in the University of Oxford. [J. Wallis and S. Ward].

  • Hobbes, Thomas, 1588-1679.
Date:
1656
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Licence: Public Domain Mark

Credit: Elements of philosophy, the first section, concerning body / Written in Latine by Thomas Hobbes of Malmesbury. And now translated into English. To which are added six lessons to the Professors of Mathematicks of the institution of Sr. Henry Savile, in the University of Oxford. [J. Wallis and S. Ward]. Source: Wellcome Collection.

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    necdTary for the generation of a Line. And though after the generation of the Line, the Point should reft, yet it is not ncccftaty from this Definition that*. it should be no mote a Point j net when Euclide defines a Sphere by the cfrcurndu&ion of a Semicircle upon an Axis that reftetb, doth it follow from thence when the Sphere, Axis, Center and all fas that cf the Earth) Is moved from place to place, that it is no moiean Axis. Laftly, you cbjed that motion is accidentary to a Point, and consequently not cffcntiall, net to be put into the Definition. And is not the circumdudion of a Semicircle acctucntary to a Sphere ? CX do you chink the Sphere of the Sun was generated by the revolution of . a Semi¬ circle ? And yet it was thought no fault in Euclide to put that motion into the Definition of a Sphere.. The conceit you have concerning Definitions, that they muft explicate the eflcncc of the thing defined, and muft confift of a genus, and a difference,is not fo univerlally true as ycu are made believe, or elfe there be. very many infiifficient Definitions that pals for goc-d with ycu in Euclide. You are much deceived if you think thefe wciull notions of yours, and the Lan¬ ge aee that doth every'where accompany them, (hew handfomely together.Or that luch grounds as thele be able to fuftain fo many, and fo haughty reproaches as you advance upon them, fo as they fall not (as you (hall fee immediately) upon your own head. I lay a point hath Quantity, but not to be reckoned in Dsmonftrating the.properties^ ot Lines, Solids, or Superficies j You fay it hath nc Quantity at all,sbut is plainly Nothing... The firft of the Petitions of Euclide is, that a Line may be drawn, from Point to Point at ary difiance. The fecond, that a ftraight Line may be produced. . The. third, that on any Center a circle may be dtferibed at any dijtance. And the eighth Axiome (which Sir H. Savile cbferves to be the foundation of all Geometry) is this, <^uat fibi mutuo congruunt, (£c. Tbofe things that arc applycd one to another in all Points, arc equall. All or any of thefe Principles being taken away, there is not in Euclide one Propofition Demonftratcd, or Demonft able. If a Point have not Quantity, a Line can have no Latitude j andbecaule a Line is not drawn but by motion, by.motioiv of a Body, and Body imprinteth Latitude all the way, it is impcflihle to draw or produce a ftraight Line, or to deferibe a circular Line without Latitude. Alfo if a Line haye no Latitude, one ftraight Line cannot be applyed to another. To them therefore that deny a Pnint to have Quantity, that is,, a Line to have Latitude, the forenamed Principles are not poffible, and£onfcqucntly no propofition in Geometry is demonftrated, or demonftrablc. - You therefore that deny, a Point to have Quantity, and a Line to have Beadth, 1 arc; nothing at all of the Science of Geometry. The praCtife you may have; but fo hath any man that hathlearned the bare Propcfitions by heart j but they arenot fit to be Profellors either of Georfietry, or of any other Science that dependeth on it. Some man perhaps may'fay that this controve.fie is not much worth, and that we both mean the lame thing. But that man (though in other things prudent enough) knoweth little of Science and Dempnftration. For Definitions are not oneiy ufed to give.us the Notions of thofe things whofe appellations are defined j for many times they that; have no Science haye the Ideas of things more perfect then fuch as are raifed by Definitions. As.who js there that imdcrftandeth not better what a ftraight Line is, or what Proportion is, - and what niany other, things are without Definition, then fome that let down the Definitions of them. But their ufe is, when they are truly and, clearly made, to draw Arguments from them for the Conclyfions to be proved. And therefore you that in ypur following cenfures of my. Geometry, .take your Argument fo often from this, That a Point is nothing, and fo often revile me for, the contrary, arc not to be allowed fuch an excufc. He that is here m-iftaken, is not to be called Negligent in his Exprefllon, but Ignorant of the Science. In the next place, you take exceptions to my Definition of Equall Bodies,which is this,Co>'- pora aqualiajunt qu& eujiicm locum poffidere pojjunt.Equall bodies are tbofe which may have the fatfcpjace. To which you objed impertinently, that I may as^vell define a man to be He that may be Prince of Tranfflvanii, Wittily, as you count wit. Formerly, in every Definition, ycu Otfded anExpUcatioiiof the E&n<& You are .therefore of ©pinion that the Poft&ility of be-