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To the READER.
GEometry is a Greek word, which in its proper signification telleth us of no other thing then Measuring of the Earth; Nevertheless, by this word we are to understand the Principal Part of the Mathematicks, which is a Science that hath for its Object Quantity continued.
A continued Quantity is that whereof all the Parts are joined together, as are all sorts of Extensions, of Greatness, and of Dimensions.
And these Dimensions consist principally either in Lines, Angles, Superficies, or Bodies, which are to be considered, not according to the Qualitie of the Matter, but ac∣cording to the Extension of the Parts.
Geometry is divided into the Theorick and the Practick. The Theorick is the Science which causeth us to conceive and demonstrate the truth of Geometrical Propositions. And the Practick is the Art which guideth the hand in its Operation.
Geometry had its beginning amongst the Egyptians, which were compelled to invent it, for to remedie the disorder that hapned ordinarilie within their Grounds, by the overflow∣ing of the River Nilus, which carried away all the Bounds, and defaced all the Limit∣marks of their Inheritances: and so this Exercise, which for the time consisted only in Measuring the Lands, for to render to every one that which belonged to him, was called the Measuring of the Earth, or Geometrie: But in process of time the Egyptians applied themselves to more subtile Enquiries, and by degrees from an Exercise altogether Mechanical, they brought forth this Excellent Science, which hath deserved to hold one of the chiefest ranks amongst all others.
Geometry is not only profitable, but we may say that it is altogether necessarie. It is by this, that the Astrologians do make their Observations by it, they know the Extent of the Heavens, the Duration of Times, the Moving of the Stars, the observation of the Sea∣sons of the Years and Ages.
It is by this Means, that the Geographers do cause us to see, at one cast of an Eye, the Greatness of the whole Earth, the huge Extension of the Seas, the Divisions of Empires, Kingdoms and Provinces.
It is from this the Architects do take their just Measures, in framing of publick Build∣ings, as well as of particular Houses.
It is by the help of this Engineers do bring to pass all their intended Projects, whereby they take the scituation and plat-form of Fortifications, the Distance of Places, and that they can at length carry their Measure through Spaces accessible only to the sight.
Persons of Qualitie, whose Birth engageth them to the Wars, are obliged to applie them∣selves to this Science. It introduceth them not only to Fortification, which teacheth them to build Bulwarks to defend strong Places, but also to compose and set up Engines, which may overthrow them; and further also it brings them very much knowledge and skill in the Military Art, how to set an Army in Order for Battel, how to encamp and divide the Ground for the quartering; and further, it teacheth them to make Maps of Countreys; and to take the Platform of Towns, Forts and Castles; to Measure all kinde of Dimensions, both accessible and unaccessible, to invent Projects; and lastly, it ma∣keth them so expert and commendable for their Wit and Inventions, as they can be for any strength or couragiousness in them.
All those that make Profession of entring upon Designs, ought to know something of Geometry, seeing that they cannot otherwise attain the Art of Architecture, nor Perspe∣ctive, which are two Parts absolutely depending on that skill.
Geometry is established upon three sorts of Principles, viz Definitions, Axioms, and Petitions.
- 1. The Definitions are brief Explications of the Names and Terms.
- 2. The Axioms are Sentences so true, and so manifest, that it is impossible to contradict them.
- 3. And the Petitions are clear and intelligible Demands, whereof the Execution and Pra∣ctice requireth not any Demonstrations.