The whole doctrine of astronomy rests upon trigonometry, a branch of the science of mathematics which teaches us, having two sides and one angle, or two angles and one side, of a triangle given us, to construct the whole. To apply this principle therefore to the heavenly bodies, it is necessary for us to take two stations, the more remote from each other the better, from which our observations should be made. For the sake of illustration we will suppose them to be taken at the extremes of the earth's diameter, in other words, nearly eight thousand miles apart from each other, the thing itself having never been realised to that extent. From each of these stations we will imagine a line to be drawn, terminating in the sun. Now it seems easy, by means of a quadrant, to find the arch of a circle (in other words, the angle) included between these lines terminating in the sun, and the base formed by a right line drawn from one of these stations to the other, which in this case is the length of the earth's diameter. I have therefore now the three particulars required to enable me to construct my triangle. And, according to the most approved astronomical observations hitherto made, I have an isosceles triangle, eight thousand miles broad at its base, and ninety-five millions of miles in the length of each of the sides reaching from the base to the apex. It is however obvious to the most indifferent observer, that the more any triangle, or other mathematical diagram, falls within the limits which our senses can conveniently embrace, the more securely, when our business is practical, and our purpose to apply the result to external objects, can we rely on the accuracy of our results. In a case therefore like the present, where the base of our isosceles triangle is to the other two sides as eight units to twelve thousand, it is impossible not to perceive that it behoves us to be singularly diffident as to the conclusion at which we have arrived, or rather it behoves us to take for granted that we are not unlikely to fall into the most important error. We have satisfied ourselves that the sides of the triangle including the apex, do not form an angle, till they have arrived at the extent of ninety-five millions of miles. How are we sure that they do then? May not lines which have reached to so amazing a length without meeting, be in reality parallel lines? If an angle is never formed, there can be no result. The whole question seems to be incommensurate to our faculties. It being obvious that this was a very unsatisfactory scheme for arriving at the knowledge desired, the celebrated Halley suggested another method, in the year 1716, by an observation to be taken at the time of the transit of Venus over the sun(50). (50) Philosophical Transactions, Vol. XXIX, p. 454.