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Lect. XV. Mathematical Lectures. 279
The third Method is by Reafoning and orga-
nical Dimenfion conjunctly, by the Labour of the
Mind and Mechanifm of the Hand. Which indeed is practical and converfant about Particulars,
yet fo as to need the help of general Theorems,
whence it is lame on one Leg, but walks direct
and certain with the other ; which, as it applies
the Rules of Geometry, has a certain Divinity and
Participation of eternal and indefectible Truth,
but as it requires mechanical Labour is fallible,
mutable, and obnoxious to Mistakes and Errors.
By this Method we not only meafure all Things
that are placed within the Reach of our Sight or
Feeling, but alfo innumerable Things inacceffible
to our Senfes, and hardly to be comprehended by
the Mind ; fuch as the Profundity and Circumference of the Earth, the Magnitudes and Inter-
ftices of the Stars, and whatfoever has any Proportion fenfibly finite with Quantities fubject to an
organical Dimenfion or inftrumental Menfuration.
For from the Proportion of the Things mechanically meafured to others exceeding that Dimenfion,
we may alfo infallibly difcover the Quantity of thefe
by help of Geometry.
Fourthly* To thefe I fubjoin the Method by
which we anfwer fuch as enquire after the Quantity of a Magnitude by really exhibiting it to the
Senfes to be estimated or to be reduced to the
Numbers of .any known Meafiure by the faid
mechanical Dimenfion. As if one afk the Quantity of a Right Line touching a propofed Circle
from a given Point. The Question will be fatisfied
in part by drawing that Right Line geometrically,
and fhewing it to the Eyes of the Querent. For
thus he will either difcern its Quantity by looking
upon it, or find to how many Particles of a known
Meafure it is precifely or nearly equal, by examining it according to fome Scale.
T 4 Th-
| Title | Usefulness of mathematical learning explained and demonstrated. |
| Alternative Title | The usefulness of mathematical learning explained and demonstrated, being mathematical lectures read in the publick schools at the University of Cambridge, by Isaac Barrow... To which is prefixed the oratorical preface of our learned author, spoke before the university on his being elected Lucasian professor of mathematics. Tr. by the Revd. Mr. John Kirkby. |
| Reference Title | Barrow, Isaac, 1734, Usefulness of mathematical learning. |
| Creator | Barrow, Isaac, 1630-1677 |
| Subject | Mathematics -- Philosophy |
| Publisher | London, S. Austen. |
| DateOriginal | 1734 |
| Format | JP2 |
| Extent | 31 cm. |
| Identifier | 1135 |
| Call Number | QA7.B3 1734 |
| Language | English |
| Collection | History of Mathematics |
| Rights | http://www.lindahall.org/imagerepro/ |
| Data contributor | Linda Hall Library, LHL Digital Collections. |
| Type | Image |
| Title | Page 279. |
| Format | tiff |
| Identifier | 1135_317 |
| Relation-Is part of | Is part of : The usefulness of mathematical learning explained and demonstrated, being mathematical lectures read in the publick schools at the University of Cambridge, by Isaac Barrow... To which is prefixed the oratorical preface of our learned author, spoke before the university on his being elected Lucasian professor of mathematics. Tr. by the Revd. Mr. John Kirkby. |
| Rights | http://www.lindahall.org/imagerepro/ |
| Type | Image |
| OCR transcript | Lect. XV. Mathematical Lectures. 279 The third Method is by Reafoning and orga- nical Dimenfion conjunctly, by the Labour of the Mind and Mechanifm of the Hand. Which indeed is practical and converfant about Particulars, yet fo as to need the help of general Theorems, whence it is lame on one Leg, but walks direct and certain with the other ; which, as it applies the Rules of Geometry, has a certain Divinity and Participation of eternal and indefectible Truth, but as it requires mechanical Labour is fallible, mutable, and obnoxious to Mistakes and Errors. By this Method we not only meafure all Things that are placed within the Reach of our Sight or Feeling, but alfo innumerable Things inacceffible to our Senfes, and hardly to be comprehended by the Mind ; fuch as the Profundity and Circumference of the Earth, the Magnitudes and Inter- ftices of the Stars, and whatfoever has any Proportion fenfibly finite with Quantities fubject to an organical Dimenfion or inftrumental Menfuration. For from the Proportion of the Things mechanically meafured to others exceeding that Dimenfion, we may alfo infallibly difcover the Quantity of thefe by help of Geometry. Fourthly* To thefe I fubjoin the Method by which we anfwer fuch as enquire after the Quantity of a Magnitude by really exhibiting it to the Senfes to be estimated or to be reduced to the Numbers of .any known Meafiure by the faid mechanical Dimenfion. As if one afk the Quantity of a Right Line touching a propofed Circle from a given Point. The Question will be fatisfied in part by drawing that Right Line geometrically, and fhewing it to the Eyes of the Querent. For thus he will either difcern its Quantity by looking upon it, or find to how many Particles of a known Meafure it is precifely or nearly equal, by examining it according to fome Scale. T 4 Th- |
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