Hi everyone,

Since I read that spherical geometry proves the Earth to be a sphere, I couldn't help but post this refutation of that allegation.

So, if the Earth were a sphere, airplane pilots would have to constantly correct their altitudes downwards so as to not fly straight off into “outer space!” If the Earth were truly a sphere 25,000 miles circumference curving 8 inches per mile squared, a pilot wishing to simply maintain their altitude at a typical cruising speed of 500 mph, would have to constantly dip their nose downwards and descend 2,777 feet (over half a mile) every minute! Otherwise, without compensation, in one hour’s time the pilot would find themselves 166,666 feet (31.5 miles) higher than expected! A plane flying at a typical 35,000 feet wishing to maintain that altitude at the upper-rim of the so-called “Troposphere” in one hour would find themselves over 200,000 feet high into the “Mesosphere” with a steadily raising trajectory the longer they go. No such compensation for the Earth’s supposed curvature is ever made. When pilots set an altitude, their artificial horizon gauge remains level and so does their course; nothing like the necessary 2,777 foot per minute declination is ever taken into consideration.

“It must be obvious to the reader that, if the earth be the globe of popular belief, the rules observed for navigating a vessel from one part of this globe to another, must be in conformity to its figure. The datum line in navigation would be an arc of a circle, and all computations would be based on the convexity of water and worked out by spherical trigonometry. Let me preface my remarks on the important branch of our subject by stating that at sea the datum line is always a horizontal line; spherical trigonometry is never used, and not one out of one thousand ship-masters understands spherical trigonometry.” -Thomas Winship, “Zetetic Cosmogeny”

Airplane pilots and sea navigators fly and sail as though the Earth were a plane. Pilots reach their desired altitude and maintain it effortlessly for hours, never contending with anything like 2,777 feet per minute of forced inclination due to Earth’s curvature. Similarly, ship captains in navigating great distances at sea, never need to factor the supposed curvature of the Earth into their calculations! Both Plane Sailing and Great Circle Sailing, the most popular navigation methods, use plane, not spherical, trigonometry.

“Plane Sailing is usually defined to be the art of navigating a ship on the supposition that the earth is a plane … even when longitude enters into consideration, it is still with the plane triangle only that we have to deal … but as the investigation here given in the text shows, the rules for plane sailing would equally hold good though the surface were a plane.”- J.R. Young, “Navigation and Nautical Astronomy”

“It must be evident to everyone who understands what a triangle is, that the base of any such figure on a globe would be an arc of a circle, of which the center would be the center of the globe. Thus, instead of a plane triangle, the figure would contain one plane angle and two spherical angles. Hence, if the plane triangle is what we have to deal with, and such is the case, the base of the triangle would be a straight line - the ocean. That all triangulation used at sea is plane, proves that the sea is a plane. The foregoing quotation states that a plane triangle is used for a spherical surface, but „the rules for plane sailing would equally hold good though the surface were a plane.‟ What fine reasoning! It is like saying that the rules for describing a circle are those used for drawing a square, but they would equally hold good though the figure were a square.” -Thomas Winship, “Zetetic Cosmogeny”

Plane Sailing is navigating a ship making all mathematical calculations on the assumption that the Earth is perfectly flat. If the Earth were in fact a sphere, such an errant assumption would lead to constant glaring inaccuracies, and the necessity for using spherical trigonometry would become obvious. Plane Sailing has worked perfectly fine in both theory and practice for thousands of years, however, and plane trigonometry has time and again proven more accurate than spherical trigonometry in determining distances across the oceans. It is so commonly used at sea; “Navigation in Theory and Practice” states that, “In practice scarcely any other rules are used but those derived from plane sailing. The great and serious objection to Plane Sailing is that longitude cannot be found by it accurately, although in practice, it is more frequently found by it than by any other method.” So both latitude and longitude are found most often and most accurately by assuming the Earth to be flat, more accurately even than assuming the Earth to be spherical!

“Plane sailing proves that the surface of water is a plane or horizontal surface and in practice it is shown that this plane extends for many thousands of miles. Whether the voyage is outwards or homewards makes no difference; thus showing that a „short voyage‟ to the Cape and back to England can be accomplished by plane sailing. The fact that water is flat like a sheet of paper (when undisturbed by wind and tide) is my „working anchor,‟ and the powerful „ground tackle‟ of all those who reject the delusions of modern theoretical astronomy. Prove water to be convex, and we will at once and forever recant and grant you anything you like to demand.” -Thomas Winship, “Zetetic Cosmogeny”

“If the Earth were a globe, a small model globe would be the very best - because the truest - thing for the navigator to take to sea with him. But such a thing as that is not known: with such a toy as a guide, the mariner would wreck his ship, of a certainty! This is a proof that Earth is not a globe … As the mariners' compass points north and south at one and the same time, and a meridian is a north and south line, it follows that meridians can be no other than straight lines. But, since all meridians on a globe are semicircles, it is an incontrovertible proof that the Earth is not a globe.” -William Carpenter, “100 Proofs the Earth is Not a Globe”

Please, offer arguments to the contrary if you have them!

Since I read that spherical geometry proves the Earth to be a sphere, I couldn't help but post this refutation of that allegation.

So, if the Earth were a sphere, airplane pilots would have to constantly correct their altitudes downwards so as to not fly straight off into “outer space!” If the Earth were truly a sphere 25,000 miles circumference curving 8 inches per mile squared, a pilot wishing to simply maintain their altitude at a typical cruising speed of 500 mph, would have to constantly dip their nose downwards and descend 2,777 feet (over half a mile) every minute! Otherwise, without compensation, in one hour’s time the pilot would find themselves 166,666 feet (31.5 miles) higher than expected! A plane flying at a typical 35,000 feet wishing to maintain that altitude at the upper-rim of the so-called “Troposphere” in one hour would find themselves over 200,000 feet high into the “Mesosphere” with a steadily raising trajectory the longer they go. No such compensation for the Earth’s supposed curvature is ever made. When pilots set an altitude, their artificial horizon gauge remains level and so does their course; nothing like the necessary 2,777 foot per minute declination is ever taken into consideration.

“It must be obvious to the reader that, if the earth be the globe of popular belief, the rules observed for navigating a vessel from one part of this globe to another, must be in conformity to its figure. The datum line in navigation would be an arc of a circle, and all computations would be based on the convexity of water and worked out by spherical trigonometry. Let me preface my remarks on the important branch of our subject by stating that at sea the datum line is always a horizontal line; spherical trigonometry is never used, and not one out of one thousand ship-masters understands spherical trigonometry.” -Thomas Winship, “Zetetic Cosmogeny”

Airplane pilots and sea navigators fly and sail as though the Earth were a plane. Pilots reach their desired altitude and maintain it effortlessly for hours, never contending with anything like 2,777 feet per minute of forced inclination due to Earth’s curvature. Similarly, ship captains in navigating great distances at sea, never need to factor the supposed curvature of the Earth into their calculations! Both Plane Sailing and Great Circle Sailing, the most popular navigation methods, use plane, not spherical, trigonometry.

“Plane Sailing is usually defined to be the art of navigating a ship on the supposition that the earth is a plane … even when longitude enters into consideration, it is still with the plane triangle only that we have to deal … but as the investigation here given in the text shows, the rules for plane sailing would equally hold good though the surface were a plane.”- J.R. Young, “Navigation and Nautical Astronomy”

“It must be evident to everyone who understands what a triangle is, that the base of any such figure on a globe would be an arc of a circle, of which the center would be the center of the globe. Thus, instead of a plane triangle, the figure would contain one plane angle and two spherical angles. Hence, if the plane triangle is what we have to deal with, and such is the case, the base of the triangle would be a straight line - the ocean. That all triangulation used at sea is plane, proves that the sea is a plane. The foregoing quotation states that a plane triangle is used for a spherical surface, but „the rules for plane sailing would equally hold good though the surface were a plane.‟ What fine reasoning! It is like saying that the rules for describing a circle are those used for drawing a square, but they would equally hold good though the figure were a square.” -Thomas Winship, “Zetetic Cosmogeny”

Plane Sailing is navigating a ship making all mathematical calculations on the assumption that the Earth is perfectly flat. If the Earth were in fact a sphere, such an errant assumption would lead to constant glaring inaccuracies, and the necessity for using spherical trigonometry would become obvious. Plane Sailing has worked perfectly fine in both theory and practice for thousands of years, however, and plane trigonometry has time and again proven more accurate than spherical trigonometry in determining distances across the oceans. It is so commonly used at sea; “Navigation in Theory and Practice” states that, “In practice scarcely any other rules are used but those derived from plane sailing. The great and serious objection to Plane Sailing is that longitude cannot be found by it accurately, although in practice, it is more frequently found by it than by any other method.” So both latitude and longitude are found most often and most accurately by assuming the Earth to be flat, more accurately even than assuming the Earth to be spherical!

“Plane sailing proves that the surface of water is a plane or horizontal surface and in practice it is shown that this plane extends for many thousands of miles. Whether the voyage is outwards or homewards makes no difference; thus showing that a „short voyage‟ to the Cape and back to England can be accomplished by plane sailing. The fact that water is flat like a sheet of paper (when undisturbed by wind and tide) is my „working anchor,‟ and the powerful „ground tackle‟ of all those who reject the delusions of modern theoretical astronomy. Prove water to be convex, and we will at once and forever recant and grant you anything you like to demand.” -Thomas Winship, “Zetetic Cosmogeny”

“If the Earth were a globe, a small model globe would be the very best - because the truest - thing for the navigator to take to sea with him. But such a thing as that is not known: with such a toy as a guide, the mariner would wreck his ship, of a certainty! This is a proof that Earth is not a globe … As the mariners' compass points north and south at one and the same time, and a meridian is a north and south line, it follows that meridians can be no other than straight lines. But, since all meridians on a globe are semicircles, it is an incontrovertible proof that the Earth is not a globe.” -William Carpenter, “100 Proofs the Earth is Not a Globe”

Please, offer arguments to the contrary if you have them!