Note: This text has been automatically extracted via Optical Character Recognition (OCR) software.
A New System Explanatory Of Terrestrial Phaenomena, &C.
being consulted about the manner of stopping a plague then raging at Athens , returned for answer , that the plague should cease when Apollo ' s Altar , which was Cubical , should be doubled . Upon this , they applied themselves , in good earnest , to seek the duplicature of the Cube , which henceforward was called the Delian Problem . The Problem is only to be solved by finding two mean proportionals between the side of the Cube , ancl double that side ; the first whereof will be the side of the
Cube doubled , as was first observed by Hippocrates Chrus . Thus let w ancl m be two mean proportionals between a and 2 a ; then a : a-:: cc : s — l f , and so : ~ : " ^ : 2 a ; therefore so = 2 a . Supposing the side ofthe given Altar a to be 10 , then the Cube root of 2 a , or 2000 , found by Approximation , will be the side of the Altar required , nearly . Eutochius , in his comments on Archimedes , gives several ways of performing this by the Mesolabe . Pappus Alexandrinusand his Commentator
, Commandine , give three ways : the first , according to Archimedes ; the second , according to Hero ; and the third , by an instrument invented by Pappus , which gives all the proportions required . The Sieur de Corniers has likewise published an elegant demonstration of the same Problem , by means of a compass with three legs ; but these methods are all onl y mechanical . " Leaving the consideration of the various methods which have been
employed to accomplish the solution of this very important problem , it remains for me to add , that the solution of the Cube ' s duplication constitutes the Apex of the Temple ; and renders a Parallelipipidon , containing 16 Linear Units , —equal to 15 Linear Units;—thus bringing the Number 16 , or fT ^ D—Messiah , —by the Musuppur Kutun , —or " shortreckoning;— fe — 40 3 into n —or 10
H )~ 300 S 5 1 — 10 8 — rr — s — is 16 358 THE GREAT NAME JAH , comprising the first two letters , of the Tetragrammaton , or ineffable NAME of DEITY nTT - —This
Duplication of the Cube , —as is demonstrated in the following Diagram , — being the finding of a mean proportional between the Radius and the Diameter , which proportional is nearly the side of no = 2 ft in Fig . 7 . I next proceed to adduce a specimen of Loadstone Rock ( Fig . 8 ) , half the natural size , likewise procured at Qutteh Ghur , in 1836 ; by which it is proved , that the Magnetic Line constitutes a perpendicular equal to the Radiusbisecting the Angle of 90 ° in a Right Angle Isoceles
, , Triangle ; ancl that the Line thereby generates the Angle of 45 ° , corresponding with the bisection of the Radius and the Co-Tangent of one Circle , and the junction of the Co-Tangent with the Tangent of another . In this Example , the situation of the Changing Points agrees with their position at the extremities of the Diameter in the square-shaped Mineral Magnet , whose delineation has already been afforded ; this specimen may he considered as constituting one-half of that Magnet .
[ JAt this interesting stage of his singular investigation , the hand of death put a stop to the labours of our much respected and deeply lamented Brother . Is there no mathematician in the Craft who can complete , e enquiries thus so nearly finished?—Ed . Freemasons' Q . R ~] VOL - vi . x x
Note: This text has been automatically extracted via Optical Character Recognition (OCR) software.
A New System Explanatory Of Terrestrial Phaenomena, &C.
being consulted about the manner of stopping a plague then raging at Athens , returned for answer , that the plague should cease when Apollo ' s Altar , which was Cubical , should be doubled . Upon this , they applied themselves , in good earnest , to seek the duplicature of the Cube , which henceforward was called the Delian Problem . The Problem is only to be solved by finding two mean proportionals between the side of the Cube , ancl double that side ; the first whereof will be the side of the
Cube doubled , as was first observed by Hippocrates Chrus . Thus let w ancl m be two mean proportionals between a and 2 a ; then a : a-:: cc : s — l f , and so : ~ : " ^ : 2 a ; therefore so = 2 a . Supposing the side ofthe given Altar a to be 10 , then the Cube root of 2 a , or 2000 , found by Approximation , will be the side of the Altar required , nearly . Eutochius , in his comments on Archimedes , gives several ways of performing this by the Mesolabe . Pappus Alexandrinusand his Commentator
, Commandine , give three ways : the first , according to Archimedes ; the second , according to Hero ; and the third , by an instrument invented by Pappus , which gives all the proportions required . The Sieur de Corniers has likewise published an elegant demonstration of the same Problem , by means of a compass with three legs ; but these methods are all onl y mechanical . " Leaving the consideration of the various methods which have been
employed to accomplish the solution of this very important problem , it remains for me to add , that the solution of the Cube ' s duplication constitutes the Apex of the Temple ; and renders a Parallelipipidon , containing 16 Linear Units , —equal to 15 Linear Units;—thus bringing the Number 16 , or fT ^ D—Messiah , —by the Musuppur Kutun , —or " shortreckoning;— fe — 40 3 into n —or 10
H )~ 300 S 5 1 — 10 8 — rr — s — is 16 358 THE GREAT NAME JAH , comprising the first two letters , of the Tetragrammaton , or ineffable NAME of DEITY nTT - —This
Duplication of the Cube , —as is demonstrated in the following Diagram , — being the finding of a mean proportional between the Radius and the Diameter , which proportional is nearly the side of no = 2 ft in Fig . 7 . I next proceed to adduce a specimen of Loadstone Rock ( Fig . 8 ) , half the natural size , likewise procured at Qutteh Ghur , in 1836 ; by which it is proved , that the Magnetic Line constitutes a perpendicular equal to the Radiusbisecting the Angle of 90 ° in a Right Angle Isoceles
, , Triangle ; ancl that the Line thereby generates the Angle of 45 ° , corresponding with the bisection of the Radius and the Co-Tangent of one Circle , and the junction of the Co-Tangent with the Tangent of another . In this Example , the situation of the Changing Points agrees with their position at the extremities of the Diameter in the square-shaped Mineral Magnet , whose delineation has already been afforded ; this specimen may he considered as constituting one-half of that Magnet .
[ JAt this interesting stage of his singular investigation , the hand of death put a stop to the labours of our much respected and deeply lamented Brother . Is there no mathematician in the Craft who can complete , e enquiries thus so nearly finished?—Ed . Freemasons' Q . R ~] VOL - vi . x x