Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	line_n	point_n	superficies_n	2,462	5	15.6907	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A44014	Six lessons to the professors of the mathematiques one of geometry the other of astronomy, in the chaires set up by the noble and learned Sir Henry Savile in the University of Oxford.	Hobbes, Thomas, 1588-1679.	1656 (1656)	Wing H2260; ESTC R22309	102,047	75

you have concerning Definitions that they must explicate the essence of the thing defined and must consist of a genus and a difference is not so universally true as you are made believe or else there be very many insufficient Definitions that pass for good with you in Euclide You are much deceived if you think these wofull notions of yours and the Language that doth every where accompany them shew handsomely together Or that such grounds as these be able to sustain so many and so haughty reproaches as you advance upon them so as they fall not as you shall see immediately upon your own head I say a point hath Quantity but not to be reckoned in Demonstrating the properties of Lines Solids or Superficies You say it hath no Quantity at all but is plainly Nothing The first of the Petitions of Euclide is that a Line may be drawn from Point to Point at any distance The second that a straight Line may be produced The third that on any Center a circle may be described at any distance And the eighth Axiome which Sir H. Savile observes to be the foundation of all Geometry is this Quae sibi mutuo congruunt c. Those things that are applyed one to another in all Points are equall All or any of these Principles being taken away there is not in Euclide one Proposition Demonstrated or Demonstrable If a Point have not Quantity a Line can have no Latitude and because a Line is not drawn but by motion by motion of a Body and Body imprinteth Latitude all the way it is impossible to draw or produce a straight Line or to describe a circular Line without Latitude Also if a Line have no Latitude one straight Line cannot be applyed to another To them therefore that deny a Point to have Quantity that is a Line to have Latitude the forenamed Principles are not possible and consequently no proposition in Geometry is demonstrated or demonstrable You therefore that deny a Point to have Quantity and a Line to have Breadth have nothing at all of the Science of Geometry The practise you may have but so hath any man that hath learned the bare Propositions by heart but they are not fit to be Professors either of Geometry or of any other Science that dependeth on it Some man perhaps may say that this controversie is not much worth and that we both mean the same thing But that man though in other things prudent enough knoweth little of Science and Demonstration For Definitions are not onely used to give us the Notions of those things whose appellations are defined for many times they that have no Science have the Ideas of things more perfect then such as are raised by Definitions As who is there that understandeth not better what a straight Line is or what Proportion is and what many other things are without Definition then some that set down the Definitions of them But their use is when they are truly and clearly made to draw Arguments from them for the Conclusions to be proved And therefore you that in your following censures of my Geometry take your Argument so often from this That a Point is nothing and so often revile me for the contrary are not to be allowed such an excuse He that is here mistaken is not to be called Negligent in his Expression but Ignorant of the Science In the next place you take exceptions to my Definition of Equall Bodies which is this Corpora aequalia sunt quae eundem locum possidere possunt Equall bodies are those which may have the same place To which you object impertinently that I may as well define a man to be He that may be Prince of Transilvania Wittily as you count wit Formerly in every Definition you exacted an Explication of the Essence You are therefore of opinion that the Possibility of being Prince of Transilvania is no less Essentiall to a man then the Possibility of the being of two Bodies successively in the same place is Essentiall to Bodies equall You take no notice of the twenty third Article of this same Chapter where I define what it is we call Essence namely that Accident for which we give the thing its name As the Essence of a man is his Capacity of reasoning the Essence of a white-body whiteness c. because we give the name of man to such Bodies as are capable of Reasoning for that their capacity and the name of White to such Bodies as have that colour for that colour Let us now examine why it is that men say Bodies are one to another Equall and thereby we shall be able to determine whether the possibility of having the same place be Essentiall or not to Bodies equall and consequently whether this Definition be so like to the Defining of a man by the Possibility of being Prince of Transilvania as you say it is There is no man besides such Egregious Geometricians as your selves that inquireth the equality of two bodies but by measure And for Liquid Bodies or the Aggregates of innumerable small Bodies men men I say measure them by putting them one after another into the same vessell that is to say into the same place as Aristotle defines place or into the space determined by the vessell as I define place And the Bodies that so fill the vessell they acknowledge and receive for equall But though when hard Bodies cannot be so measured without the incommodity or trouble of altering their Figure they then enquire if the Bodies are both of the same kind their equality by weight knowing without your teaching that equall bodies of the same nature weigh Proportionably to their magnitudes yet they do it not for fear of missing of the equality but to avoid inconvenience or trouble But you you I say that have no Definition of Equalls neither received from others nor framed by your selves out of your shallow meditation and deep conceit of your own Wits contend against the common light of Nature So much is unheedy learning a hinderance to the knowledge of the truth and changeth into Elves those that were beginning to be men Again when men inquire the equality of two Bodies in length they measure them by a common measure in which measure they consider neither breadth nor thickness but how the length of it agreeth first with the length of one of the Bodies then with the length of the other And both the Bodies whose lengths are measured are successively in the same place under their common measure Place therefore in Lines also is the proper Index and discoverer of Equality and Inequality And as in length so it is in breadth and thickness which are but Lengths otherwise taken in the same Solid Body But now when we come from this Equality and Inequality of Lengths known by measure to determine the Proportions of Superficies and of Solids by ratiocination then it is that we enter into Geometry for the making of Definitions in whatsoever Science