Sentinel of the valley. [volume] (Woodstock, Va) 1841-1848, 1845-11-20
FOR THE sENTEssSl
NO PROTEUS, BUT PROTEROS

Ostay at school, young Truant Of the Lawn
On devious paths thy Grant feet are drawn.
The boy Dadalian from the Gnosslan cline,
Took wings of wax, and tried the blue sublime;
The sun was hot, as old historians tell,
And poor Icarus on the pillows fell.
Beware, my boy, else thus it prove with thee.
For rod and Isuant never could agree.
Didst make frame, an oser plat design.
With curve and chord, ami lgament and litls2
Two lateral rods thy sedgmenis separate,
One eighty-fve, the other sixty eight,
Two rigid chords the circular arcs subrend,
! Embrace the rods, and clasp them end BY end,
This fifty one, and that just twice As long;
| Neat was the labor, and the structure strong.
But 10 alas! extend your hands and cape!
The wondrous ff'aaae had neither form nor shaps
! And, oh forgive Us, great Archmedes,
There were some angles. but without degrees,
0 wondrous frame, o structure nicely done!
| Ten thousand shapes, yet not single one n!
Those barbarous curves they pulled it sll awry.
| wonder if the Truant didn', ery,-
| There all alone and fated to behold
The mighty magic of the gods of cid.
Come now, my truant boy, and let US see
| If any author will with us agree.
All have maintained three given sides will do
| In triangles to find the angles too;
| And Bonnycastle has the rule applied,
| When four are given, such as thou hast tried
-Four lines gave thee, definite and straight,
A neat trapezium. called frame Of late.
Come draw the lines, The plat when rightly done,
Will have one form, and have but only one
Square one and fifty, eight and sixty s9nare,
! These squares with that Of eighty five compare:
| The sum If those and square Of this agree,
| Hence sums of angles opposite must etual BE-
Dismiss thy fears.-all bubbles, quirks ioIego;
Old Shenandoah will solve i, yet, know.
- A. NJ
*At page 223 of his Mensuration, Bonny
castle has given the following problem:
The four side Of field, whose diagonals
are equal 10 each other, are Is, 50, 81, aud
10 poles, respectively; what is the area?
cans FAC. lro. 50 poles"
Mr.. Bonnycastle further observes, in note
to the construction Of this probem-''This me
thod is applicable to all questions of the kind,
wherein the diagonals cross each other at right
angles; that is, when the sums of the squares
Of the opposite sides are equal, but general So
luton to the question, without this, would in
vove an equation of the higher order
n. B. He does not say, ,co,sld be mlossible,
hut, '',rould incolre an equation Of the higher
order" Now, we know that numerical equa-
| tons ofall orders are CAPABLE of solution. The
difficulties of our problem might therefore he
increased a hundred fold. and still to complete
| y within the powers of analysis. Indeed, the
bearings or angles would be of little service in
this case, for the difficulty does not lie in find
ing the area. And how should we have given
the bearings Of the arcs2 The practical sur
veyor, perhaps, would take offsets but he
| must know, that in valuable land very seri-
Gus loss would be sustained by this method
Our object is, that the principles employed
shall be rigidly true.