New Elements of GeometryG.P. Putnam, 1850 - 200 Seiten |
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ABCD agreeably area equals one-fourth area equals one-half area equals three-fourths arithmetical calculation breadth circum circumference is four circumference is three cone contained in ABFG cubic inch cumference cylinder DBCE demonstrations diagonal diagram diame diameter is four equal heights equal rectangles equal triangles equals one-third equals the area equals the circumference equals the diameter equals the square equals the surface equals two-thirds equilateral triangle face ference four equal geometrical quantity geometrical unit geometry half the arc hypothenuse infinitely inscribed circle inscribed sphere length line of circumference linear edge lines drawn mathematical measure mixed mathematics multiplied numbers octahedron parallelogram perfect cube perpendicular plane figure polygon principles Prop proposition Pythagoras radius rectangle ABFG regular hexagon regular octagon regular pentagon right angle SEBA SMITH side slant height solid figures solidity equals surface equals tetrahedron thickness triangle ABC triangle equals Twice the square unit whole circumference
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Seite 15 - This kind of degenerate learning did chiefly reign amongst the schoolmen, who, having sharp and strong wits, and abundance of leisure, and small variety of reading ; but their wits being shut up in the cells of a few authors, chiefly Aristotle their dictator, as their persons were shut up in the cells of monasteries and colleges, and knowing little history, either of nature or time, did, out of no great quantity of matter, and infinite agitation of wit, spin out unto us those laborious webs of learning,...
Seite 23 - For the wit and mind of man, if it work upon matter, which is the contemplation of the creatures of God, worketh according to the stuff, and is limited thereby; but if it work upon itself, as the spider worketh his web, then it is endless, and brings forth indeed cobwebs of learning, admirable for the fineness of thread and work, but of no substance or profit.
Seite 200 - Prescient, the tides or tempests to withstand, Build on the wave, or arch beneath the sand ? Who made the spider parallels design, Sure as De Moivre, without rule or line...
Seite 70 - In the mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For, if the wit be dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it.
Seite 73 - ... and seldom sincerely to give a true account of their gift of reason, to the benefit and use of men: as if there were sought in knowledge a couch, whereupon to rest a searching and restless spirit; or a terrace, for a wandering and variable mind to walk up and down with a fair prospect; or a tower of state, for a proud mind to raise itself upon; or a fort or commanding ground, for strife and contention; or a shop, for profit or sale; and not a rich storehouse, for the glory of the Creator and...
Seite 17 - It is necessary to consider a solid, that is, a magnitude which has length, breadth, and thickness, in order to understand aright the definitions of a point, line and superficies ; for these all arise from a solid, and exist...
Seite 23 - Lives through all life, extends through all extent, Spreads undivided, operates unspent ; Breathes in our soul, informs our mortal part, As full, as perfect in a hair as heart ; As full, as perfect in vile man that mourns, As the rapt seraph that adores and burns. To Him no high, no low, no great, no small ; He fills, He bounds, connects and equals all.
Seite 73 - For men have entered into a desire of learning and knowledge, sometimes upon a natural curiosity and inquisitive appetite ; sometimes to entertain their minds with variety and delight ; sometimes for ornament and reputation ; and sometimes to enable them to victory of wit and contradiction; and most times for lucre and profession ; and seldom sincerely to give a true account of their gift of reason, to the benefit and use of men...
Seite 61 - The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it...
Seite 71 - ... mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull they sharpen it; if too wandering, they fix it ; if too inherent in the sense they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures ; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.