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NORTHFIELD, VT., MAR. 25, 1874, EXPLANATIONS TO THE GENERAL READER. 2. To Demonstrate a GEOMETRICAL THEOREM the magnitudes used in the work are assumed, generally, and their several combinations must be made according to previously established propositions, by a strictly logical method; so that the final conclusion shall be as completely established, as is each and every proposition on which the demonstration depends. S. To Solve, a GEOMETRICAL PROBLEM the mag. r.itudes used in the solution are given, particularly, and their several combinations must be made according to previously established principles, with j appropriate mathematical instruments; then the accuracy of the final result will depend, wholly, upon the perfection of the instruments and correctness of their application. In short.— A GEOMETRICAL THEOREM is a proposition intended to establish, by a logical process, a general result from assumed data. A GEOMETRICAL PROBLEM is a proposition intended to establish, by instrumental construction, a particular result from given data. FIRST QUESTION CONSIDERED. 4. To SQUARE THE CIRCLE, two distinct operations are required:— First.— To demonstrate the principle by which assumed data, pertaining to any circle may be combined, so as to produce a square whose area shall be equal to that circle, (2.) Second. — To solve the problem by which given liaui j*:!;;,!:; .g ia u circle may {>?«.*« in strumental!} combined, as to construct a square equivalent to that circle,'(3.) 5. Now in solving geometrical problems which pertain to plane rectilinearjfigures, it is well known to geometers :— First.— That any two®figures being given, a third may be constructed which shall be similar to one of the two, and equivalent to the other. Second.—That any figure may have its equivalent square constructed. Third.—That a square jta be constructed which shall be equivalent to the sum, or to the difference, of any two squares. It hence follows, that the sum — or the difference— of any two rectilinear plane figures, may be transformed to an equivalent one of any desirable shape. Now it will be seen that circles are not included among the rectilinear figures mentioned above, yet it is evident that if circles eotald be "squared,"— also the square reduced to an equivalent circle—then circles in common with rectilinear plane figures would all enjoy, equally, the general transmutation ; and it was upon the strength of this very principle that the SQUARE OF THE CIRCLE was so ardently desired by the Ancients. EDITORS FOR 2D TEH:,! 1174. J. K. STEARNS, G.H.I). THOMAS CHARLES WILLIAM IL,RRT 1? CARRINGTON I. HAYES, P. WILLIAM R. CURTIS,  A. WILLIAM T. SPRAGUE, R. MEMBERS, Archie Lorenzo Sheldon, West Rutland. William Hooper, Boston, Mass. Edward l';<ncost Pitman, Malone, N.Y. Charles James Luck, Rouse's Point, " Benjamin Ball Newton, Brooklyn, " Arnold Thayer, " " Frank Henry Reed, Greenfield, Mass. William Tolman Sprague, Boston, " Frank Richard Bates, * Northfield. Carrington Isaac Hayes, Unadilla, N. Y. William Herbert Tucker, West Hartford, Loomis Stevens Cull, Belvedere. James Wheeler Swett, Fairfax. William Moser Rumbaugh, Mt. Pleasant, Pa, Eben Barlow Jewell, St. Albans, George Ellery Loomis, Jackson, Mich. William Henry Saxe, St. Albans. George Edward Edson, " Harry Bates Thayer, Northfield. William Russell Curtis, Yarmouth, Me. Edgar Sands Turton, Sands Point, L. I. George Henry Delbert Thomas, Northfield. ROBERT A. SILVER, JOHN K. STEARNS, DAVID B. DOUGLASS HARRY C. DOLE, Northfield, Xlighgate Center, Northfield. West Randolph, Northfield, Langdon, N. H, Rutland. New York, Swanton. Northfield, Robert Alexander Silver, John Andrew Lookinland, John Kerswell Stearns, Edwaril Denslow Upham, George Wells Hadley. Harlie Jackson Huntoon, Charles lvilburn Williams, Waldo Henry Richardson. Solon Adams, Benjamin Hale Douglass, David Bates Douglass, " Louis Edward Johnson, Whitehall, N. Y. Harry Christopher Dole, Northfield. John Kellogg Waite, Norwich, N. Y. Theodore Chardavoyne Mcllwaine, Essex, " Frank Clark Hatch, Woodstock. These societies occupy commodious, well furnished halls down town, the Theta Chi in Central Block, and the Alpha Sigma Pi in Depot Block. They were organized and are maintained for literary purposes. Friday evenings, from 6 to 10 P. M., are allowed for society meetings. Northfield. Robert Manson Stephens, " Charles Edward Field, William Henry Ferris, Ilackettstown, N. J. Greenfield, Mass. Northfield. "THE CIRCLE SQUARED," BY PROF. A. JACKMAN. INTRODUCTION. 1. The questions most likely to be proposed concerning this subject are :— First.—What is to be understood by "SQUARING THE CIRCLE?" and, what is the benefit to be derived from its accomplishment? Second.—Has the Circle been Squared ? These questions are to be considered in the following :— SECOND QUESTION CONSIDERED, WITH A SHORT HISTORIC PREFACE. 6. Century after century passed while ancient geometers were anxiousiy searching for the desired solution; yet the circle was not squared. However, in their investigations they made the important discovery that the an a of any circle contains the square of its radius at many times as its circumference contains its diameter; but, to find this remarkable number constituted a second problem ; wherefore, they found thqy had two difficult problems on their hands. Far convenience, this remarkable number will hert be called the CIRCUMMETRIC RATIO, and its ciact value, though unknown, be denoted by the Greek letter •k. (Concluded on ftmrtli page.) VOL. XL. NO. 2. MEMBERS, OFFICERS, E. 0. E. 0. X. X. 0. X. E. 0. E. D. UPHAM, PublS, EH. PUBLIS II E I) BY IB K CADETS OF NORWICH J VERSITY,
Object Description
Title  Reveille, Volume XL, Issue 2 
Date  18740325 
Creator  Norwich University 
Publisher  Norwich University 
Subject  Places  Northfield (Vt.); 
Format, Original  4 pages ; 30 x 23 cm. 
Format, Digital  application/pdf 
Identifier  RvXL_2_1874 
Location of original  Newspapers & Magazines Collection 
Digitized by  Norwich University Archives 
Rights  This digital file is provided for educational purposes only. Further information about copyright and reproductions may be obtained from Norwich University Archives. 
Repository  Norwich University Archives, Kreitzberg Library, 158 Harmon Drive, Northfield, VT 05663 
Description
Title  Page 1 
Date  18740325 
Creator  Norwich University 
Publisher  Norwich University 
Subject  Places  Northfield (Vt.); 
Format, Original  4 pages ; 30 x 23 cm. 
Format, Digital  application/pdf 
Identifier  RvXL_2_1874 
Location of original  Newspapers & Magazines Collection 
Digitized by  Norwich University Archives 
Rights  This digital file is provided for educational purposes only. Further information about copyright and reproductions may be obtained from Norwich University Archives. 
Repository  Norwich University Archives, Kreitzberg Library, 158 Harmon Drive, Northfield, VT 05663 
Full Text 
NORTHFIELD, VT., MAR. 25, 1874,
EXPLANATIONS TO THE GENERAL READER.
2. To Demonstrate a GEOMETRICAL THEOREM the magnitudes used in the work are assumed, generally, and their several combinations must be made according to previously established propositions, by a strictly logical method; so that the final conclusion shall be as completely established, as is each and every proposition on which the demonstration depends.
S. To Solve, a GEOMETRICAL PROBLEM the mag. r.itudes used in the solution are given, particularly, and their several combinations must be made according to previously established principles, with j appropriate mathematical instruments; then the accuracy of the final result will depend, wholly, upon the perfection of the instruments and correctness of their application.
In short.— A GEOMETRICAL THEOREM is a proposition intended to establish, by a logical process, a general result from assumed data.
A GEOMETRICAL PROBLEM is a proposition intended to establish, by instrumental construction, a particular result from given data.
FIRST QUESTION CONSIDERED.
4. To SQUARE THE CIRCLE, two distinct operations are required:—
First.— To demonstrate the principle by which assumed data, pertaining to any circle may be combined, so as to produce a square whose area shall be equal to that circle, (2.)
Second. — To solve the problem by which given liaui j*:!;;,!:; .g ia u circle may {>?«.*« in
strumental!} combined, as to construct a square equivalent to that circle,'(3.)
5. Now in solving geometrical problems which pertain to plane rectilinearjfigures, it is well known to geometers :—
First.— That any two®figures being given, a third may be constructed which shall be similar to one of the two, and equivalent to the other.
Second.—That any figure may have its equivalent square constructed.
Third.—That a square jta be constructed which shall be equivalent to the sum, or to the difference, of any two squares.
It hence follows, that the sum — or the difference— of any two rectilinear plane figures, may be transformed to an equivalent one of any desirable shape.
Now it will be seen that circles are not included among the rectilinear figures mentioned above, yet it is evident that if circles eotald be "squared,"— also the square reduced to an equivalent circle—then circles in common with rectilinear plane figures would all enjoy, equally, the general transmutation ; and it was upon the strength of this very principle that the SQUARE OF THE CIRCLE was so ardently desired by the Ancients.
EDITORS FOR 2D TEH:,! 1174.
J. K. STEARNS, G.H.I). THOMAS
CHARLES WILLIAM IL,RRT 1?
CARRINGTON I. HAYES, P.
WILLIAM R. CURTIS,  A.
WILLIAM T. SPRAGUE, R.
MEMBERS,
Archie Lorenzo Sheldon, West Rutland.
William Hooper, Boston, Mass.
Edward l'; 
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