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A New System Explanatory Of Terrestrial Phaenomena, &C.
is bisected in C ; and A C A E being Radii of the same Circle , ACE are equal ; and A E being bisected in C , A F , the Line terminated by the circumference of the Circle 0 90 0 , is a fraction greater than A G , — the of A E . Wherefore , the whole line B F is equal to 2 | X a fraction ; ancl is yet less than 2 § ; and is , accordingly , an approximation to 3 ^ 16 , the side of the required Cube . It will likewise be remarked , that as the side of a 2 a depends the finding of two
; = , upon mean Proportionals between the side of a ? ancl 2 a , the first of which shall be the side of the required Cube , so do we reach the knowledge of the fact , by means of Magnetic , Geological Geometry , that in a Semicircle , whose diameter is made equal to 4 , the side of a = 8 , being raduis = 2 ; and consequently 2 a = 16 , two mean Proportional Lines are found in the Sines of the Angles of 60 ° and 70 " , or those of the Polar Points in the True Circleand Curve of the Earth ' s Spheroidwhich evolve a
, , Segment of the Diameter , constituting an Hypotheneuse , common to two Right-Angled Triangles , which Segment is equal to the side of sc = 2 a ; a segment that is moreover nearly equal to the Chord of 85 "; the point at which the Hypotheneuse D B ( in a former Diagram ) of the 67 ^ Tangential Right-Angled Triangle , cuts the circumference of the Circle . Thus , let C D ( Fig . 6 ) , the Diameter of the Circle C A E D H , be an Hypotheneuse common to the two Right-Angled Triangles CAD , 3
D E C , and both equal to 4 ; and the side of 2 a = 16 . Then A B , or Sine of 60 ° , in the Semicircle , 0 90 0 , is a mean Proportional between C B and B D ; and E F , the Sine of 70 ° , in the same Semicircle , is a mean Proportional between D F and F C . But C F , a Segment of the Hypotheneuse C D , is cut off from the Diameter , by the circumference of the Circle A F I , having A B , the Sine of 60 ° , for Radius ; while E F , the Sine of 70 ° , meeting the Diameter in the Point , F is Tangent to the
same Circle . Now C F is a Segment of the Diameter greater than 2 Cosines and ^ , and less than 2 Cosines and J of a Cosine ; C F is , therefore , the side of a- = 2 a , or approximates 3 A / 16 ; and this Segment is evolved by the Circumference of the Circle having for Radius the Sine of 60 ° , and by the Sine of 70 " , which is Tangent to the same Circle ; those Sines being two mean Proportionals , in the Semicircle of which C D is the Diameter ; and C F being moreover equal to C 85 , because it is Radius of the Circle C 85 F K .
Wherefore , by an acquaintance with the Geological , Geometrical Science , impressed upon the Magnetic Rocks , clo we arrive at the knowledge of the astounding truth , that , in the difference of proportion between the form of the Earth ' s Spheroid and the Curve of a true Circle , exist two Mean Proportional Lines , which are capable of solving the celebrated Problem of the Cube ' s Duplication ; by furnishing tbe construction of a Cube , whose solid contents shall be an approximation to those of two given Cubes ; and hence , as the sides of every two Cubes
may be made tbe Diameter of a Circle , here is discovered an Universal Rule for tbe solution of the Cube ' s Duplication . As it is upon the solution of this Problem , that the construction of THE TEMPLE depends , I shall , in this place , give the following account of the origin and history of this most celebrated Proposition , —as it exists in Chambers' Cyclopcedia , Article , " DUPLICATION OF THE CUBE . " " DUPLICATION OF A CUBE , is the finding the side of a Cube that shall be double in solidity to a given Cube ; which is a famous Problem cultivated by the Geometricians two thousand years ago . "It was first proposed by the Oracle of Apollo , at Delphos ; which
Note: This text has been automatically extracted via Optical Character Recognition (OCR) software.
A New System Explanatory Of Terrestrial Phaenomena, &C.
is bisected in C ; and A C A E being Radii of the same Circle , ACE are equal ; and A E being bisected in C , A F , the Line terminated by the circumference of the Circle 0 90 0 , is a fraction greater than A G , — the of A E . Wherefore , the whole line B F is equal to 2 | X a fraction ; ancl is yet less than 2 § ; and is , accordingly , an approximation to 3 ^ 16 , the side of the required Cube . It will likewise be remarked , that as the side of a 2 a depends the finding of two
; = , upon mean Proportionals between the side of a ? ancl 2 a , the first of which shall be the side of the required Cube , so do we reach the knowledge of the fact , by means of Magnetic , Geological Geometry , that in a Semicircle , whose diameter is made equal to 4 , the side of a = 8 , being raduis = 2 ; and consequently 2 a = 16 , two mean Proportional Lines are found in the Sines of the Angles of 60 ° and 70 " , or those of the Polar Points in the True Circleand Curve of the Earth ' s Spheroidwhich evolve a
, , Segment of the Diameter , constituting an Hypotheneuse , common to two Right-Angled Triangles , which Segment is equal to the side of sc = 2 a ; a segment that is moreover nearly equal to the Chord of 85 "; the point at which the Hypotheneuse D B ( in a former Diagram ) of the 67 ^ Tangential Right-Angled Triangle , cuts the circumference of the Circle . Thus , let C D ( Fig . 6 ) , the Diameter of the Circle C A E D H , be an Hypotheneuse common to the two Right-Angled Triangles CAD , 3
D E C , and both equal to 4 ; and the side of 2 a = 16 . Then A B , or Sine of 60 ° , in the Semicircle , 0 90 0 , is a mean Proportional between C B and B D ; and E F , the Sine of 70 ° , in the same Semicircle , is a mean Proportional between D F and F C . But C F , a Segment of the Hypotheneuse C D , is cut off from the Diameter , by the circumference of the Circle A F I , having A B , the Sine of 60 ° , for Radius ; while E F , the Sine of 70 ° , meeting the Diameter in the Point , F is Tangent to the
same Circle . Now C F is a Segment of the Diameter greater than 2 Cosines and ^ , and less than 2 Cosines and J of a Cosine ; C F is , therefore , the side of a- = 2 a , or approximates 3 A / 16 ; and this Segment is evolved by the Circumference of the Circle having for Radius the Sine of 60 ° , and by the Sine of 70 " , which is Tangent to the same Circle ; those Sines being two mean Proportionals , in the Semicircle of which C D is the Diameter ; and C F being moreover equal to C 85 , because it is Radius of the Circle C 85 F K .
Wherefore , by an acquaintance with the Geological , Geometrical Science , impressed upon the Magnetic Rocks , clo we arrive at the knowledge of the astounding truth , that , in the difference of proportion between the form of the Earth ' s Spheroid and the Curve of a true Circle , exist two Mean Proportional Lines , which are capable of solving the celebrated Problem of the Cube ' s Duplication ; by furnishing tbe construction of a Cube , whose solid contents shall be an approximation to those of two given Cubes ; and hence , as the sides of every two Cubes
may be made tbe Diameter of a Circle , here is discovered an Universal Rule for tbe solution of the Cube ' s Duplication . As it is upon the solution of this Problem , that the construction of THE TEMPLE depends , I shall , in this place , give the following account of the origin and history of this most celebrated Proposition , —as it exists in Chambers' Cyclopcedia , Article , " DUPLICATION OF THE CUBE . " " DUPLICATION OF A CUBE , is the finding the side of a Cube that shall be double in solidity to a given Cube ; which is a famous Problem cultivated by the Geometricians two thousand years ago . "It was first proposed by the Oracle of Apollo , at Delphos ; which