DOI Page / Citation link:
https://doi.org/10.11588/diglit.62828#0064
for him to know. For inftance, he needs not be told that a
point is without parts or magnitude, that a line is length
without breadth, or that the terms of a line are points, 8cc.
Thefe, and a number of others of this kind, are known by the
common underftanding of every one. I fhall therefore confine
myfelf to fuch particulars as every candid workman will at once
pronounce ufeful, and which may be applied to the practice of
home parts of the ingenious art of Cabinet-making. Yet, from
what I have here advanced with refpedt to geometrical defini-
tions, I would not be underftood as fpeaking difrefpedtfully of
them, much lefs to deny their ufefulnefs to fuch as learn geo-
metry regularly. It is impoflible to proceed without thefe,
when this ancient and divine fcience is taught as the ground-
work of mathematical learning. We might as well attempt to
teach logic without a method of arranging or diftinguifhing
ideas, or arithmetic without the powers and properties of num-
bers, as geometry divefted of its chain of definitions and axioms,
See. by which at length we arrive to the certain knowledge of
truth, and are able to demonftrate it to others. But, on the
other hand, as it is poflible for a man of found fenfe to reafon
well without knowing the rules of logic as they are taught in
fine and regular fyftems, fo, I apprehend, it is alfo poflible for a
workman of no learning, but what is common, to attain to a
ufeful knowledge of geometrical lines, without the trouble of
going through a regular courfe of Euclid’s definitions and de-
monftrations,
point is without parts or magnitude, that a line is length
without breadth, or that the terms of a line are points, 8cc.
Thefe, and a number of others of this kind, are known by the
common underftanding of every one. I fhall therefore confine
myfelf to fuch particulars as every candid workman will at once
pronounce ufeful, and which may be applied to the practice of
home parts of the ingenious art of Cabinet-making. Yet, from
what I have here advanced with refpedt to geometrical defini-
tions, I would not be underftood as fpeaking difrefpedtfully of
them, much lefs to deny their ufefulnefs to fuch as learn geo-
metry regularly. It is impoflible to proceed without thefe,
when this ancient and divine fcience is taught as the ground-
work of mathematical learning. We might as well attempt to
teach logic without a method of arranging or diftinguifhing
ideas, or arithmetic without the powers and properties of num-
bers, as geometry divefted of its chain of definitions and axioms,
See. by which at length we arrive to the certain knowledge of
truth, and are able to demonftrate it to others. But, on the
other hand, as it is poflible for a man of found fenfe to reafon
well without knowing the rules of logic as they are taught in
fine and regular fyftems, fo, I apprehend, it is alfo poflible for a
workman of no learning, but what is common, to attain to a
ufeful knowledge of geometrical lines, without the trouble of
going through a regular courfe of Euclid’s definitions and de-
monftrations,