ENUCLID'S ELEMENTS, or Second Les
lL snna In GeomefrY in the order of Simaon,s q
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LNUCLID'S ELEMENTS, or Second Les
IL sons In Geometry, in the order of Simson's
| r.nced learners and pfiv.s. -s.a.na. by D. McCur-
uy, autuor OF the --Cha,t vr deoue., ~
Lessons" Collins Brother Co., 254 Pearl street,
New York, publishers.


These works are designed TO extend and facilitate
the study Of geometry in the schools. The chart
exhibits the diagrams Of ak books of Euclid plane
trigonometry, and the quadrature Of the circle
large scale, mounted in two parts, map. The
book called First Lessons contains the entire text
with references 10 the proofs used in the demonstra-
tons; and the book first above mentioned contains
the demonstrations complete, and is equivalent to
Playfar's Euclid.


The chart and first lessons present these elements
in the only form in which they can be made gen.
eraI basis of school instruction. and such they ought
to be, because they enter all the affairs of men,
either as coadjutor Of every useful art or as a
model of reasoning on every subject of human
knowledge The plan here proposed will restrain
the skifu geomeler, when he would run too far in
advance of his pupils; and the less proficient will
find in IT no more than can be reduced to practice
namely, the readings and recations of the PROPOSE
tons, which any reader may perform, and which
are to be illustrated by drawing the appropriate d-
ae rams states in the sand.


In the Grccian schools geometry preceded arth-
meuc and that with great proprley; for next TO the
arts OF reading and writing, which but new
modes OF receiving instruction, those properties of
things which are the first subjects of observation
and experiment claim the first consideration But
magnitude, figure, and motion are the most imposing
properties Of things and geometry presents these in
miniature, or acts upon them in their natural forms
and dimensions, so that they furnish the most suit
able exercise for the juvenile mind. Geometry is
called higher department of oflearning only for want
of the proper distinction between the elements and
their application.


In allusion to the pecuartes of the book first
above mentioned. II n he aDpcific.


believed to contain all the elements, and it affords
room for dllutlng the subject. The order of Eu-
cid has been preserved, because it has never been
exceed; but the repetitons which swell other
editlonsr perpex the learner, and defeat the end,
are Eere obviated by the plan of previous reci-
tatons. The demonstrations of the fifth book have
been simpfed exceedingly, not by the substitution
Of symbols for words, but by definition of ra-
to- and Sigh alteration in the method of compound


ing ratios. Nevertheless, has been taken intro
duce nothing which could not be directly employed
in drawing out the properties of proportionals ac-
| cordipg 70 tho tisor Of the Euolidan geometry.
The change consists in fixing definitely the value of
ratio according TO its general in the mathemat-
les.


There is solemn voice in the natural truths OF
geometry which calls upon school officers, princi-
pals and teachers to the seed to scnter il broad
| cast over this national husbandry; that voice is
tremuons with the fears and hopes of the future
harvest There ia hand which points to the per-
durable maxim, "Whatsoever man sows, that
shall he also reap" Ifa nation SOW the seed of er-
ror, Its enclosures shall be neglected, and its paths
underlined If the seed of truths az contained in &c.
ometry, the laws Of nature in all her departments
Will be respected, and the blessings of wise popu-
lar government will endure as long as the sun and
| moon.


Hundreds Of intelligent citizens have seen the
Chart of Geometry and book of First Lessons, and
accord to he system thir unqualified appreciation.


April 3t-eo7t