Astronomers From England

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April 10, 2026

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April 10, 2026

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"It would seem at first sight as if the rapid expansion of the region of mathematics must be a source of danger to its future progress. Not only does the area widen but the subjects of study increase rapidly in number, and the work of the mathematician tends to become more and more specialized. It is, of course, merely a brilliant exaggeration to say that no mathematician is able to understand the work of any other mathematician, but it is certainly true that it is daily becoming more and more difficult for a mathematician to keep himself acquainted, even in a general way, with the progress of any of the branches of mathematics except those which form the field of his own labours. I believe, however, that the increasing extent of the territory of mathematics will always be counteracted by increased facilities in the means of communication. Additional knowledge opens to us new principles and methods which may conduct us with the greatest ease to results which previously were most difficult of access; and improvements in notation may exercise the most powerful effects both in the simplification and accessibility of a subject. It rests with the worker in mathematics not only to explore new truths, but to devise the language by which they may be discovered and expressed; and the genius of a great mathematician displays itself no less in the notation he invents for deciphering his subject than in the results attained.... I have great faith in the power of well-chosen notation to simplify complicated theories and to bring remote ones near and I think it is safe to predict that the increased knowledge of principles and the resulting improvements in the symbolic language of mathematics will always enable us to grapple satisfactorily with the difficulties arising from the mere extent of the subject"

- James Whitbread Lee Glaisher

• 0 likes• university-of-cambridge-alumni• university-of-cambridge-faculty• mathematicians-from-england• people-from-london• astronomers-from-england•
"Quite distinct from the theoretical question of the manner in which mathematics will rescue itself from the perils to which it is exposed by its own prolific nature is the practical problem of finding means of rendering available for the student the results which have been already accumulated, and making it possible for the learner to obtain some idea of the present state of the various departments of mathematics.... The great mass of mathematical literature will be always contained in Journals and Transactions, but there is no reason why it should not be rendered far more useful and accessible than at present by means of treatises or higher text-books. The whole science suffers from want of avenues of approach, and many beautiful branches of mathematics are regarded as difficult and technical merely because they are not easily accessible.... I feel very strongly that any introduction to a new subject written by a competent person confers a real benefit on the whole science. The number of excellent text-books of an elementary kind that are published in this country makes it all the more to be regretted that we have so few that are intended for the advanced student. As an example of the higher kind of text-book, the want of which is so badly felt in many subjects, I may mention the second part of Prof. Chrystal’s “Algebra” published last year, which in a small compass gives a great mass of valuable and fundamental knowledge that has hitherto been beyond the reach of an ordinary student, though in reality lying so close at hand. I may add that in any treatise or higher text-book it is always desirable that references to the original memoirs should be given, and, if possible, short historic notices also. I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."

- James Whitbread Lee Glaisher

• 0 likes• university-of-cambridge-alumni• university-of-cambridge-faculty• mathematicians-from-england• people-from-london• astronomers-from-england•
"I have lately spent some Thoughts relative to the Nature of Light, whether it be subject to the common Laws of Motion. In this particular Newton seems to contradict himself. For in his Principia Sect. 14th he applies the common Laws of Motion to account for Reflection and Refraction, as he does also in one Part of his Optics where he proves the Sine of Incid. to Sine Refr, in a given in a given Ratio. But in another Part he says, “nothing more is requisite for producing all the Variety of Colours and Degrees of Refrangibility than that the Rays of Light be Bodies of different Sizes, the least of which may make Violet, and the Greatest the Red"; this manifestly is not consistent with the Theory of Motion applied to Bodies, where the Magnitude of the Bodies is of no Consequence. Now it is evident that if the common Theory of Motion can be applied to Light, the Red Light must have had the greatest Velocity before Incidence, as it suffers the least Deviation, for if the Vels of all the Difft colour'd Light were equal before Incidence, they must by Newton's Principia Sect. Sect. 8. Prop. 1. have continued equal after, and therefore must have suffered the same Deviation. The Determination of this Point seems to be of considerable Importance, as we so often apply the Theory of Motion to Light."

- Samuel Vince

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"The rapid establishment of Christianity must therefore have been from the conviction which those who embraced it, had of its "Truth and power unto salvation." Christianity at first spread itself amongst the most enlightened nations of the earth - in those places where human learning was in its greatest perfection; and, by the force of the evidence which attended it, amongst such men it gained an establishment. It has been justly observed, that "it happened very providentially to the honour of the Christian religion, that it did not take its rise in the dark illiterate ages of the world, but at a time when arts and sciences were t their height, and when there were men who made it the business of their lives to search after truth and lift the several opinions of the philosophers and wise men, concerning the duty, the end, and chief happiness of reasonable creatures." Both the learned and the ignorant alike embraced its doctrines; the learned were not likely to be deceived in the proofs which were offered; and the same cause undoubtedly operated to produce the effect upon each. But an immediate conversion of the bulk of mankind, can arise only from some proofs of a ddivine authority offering themselves immediately to the senses; the preaching of any new doctrine, if lest to operate only by its own force, would go but a very little way towards the immediate conversion of the gnorant, who have no principle of action but what arises from habit, and whose powers of reasoning are insufficient to correct their errors. When Mahomet was required by his followers to work a miracle for their conviction, he always declined it; he was too cautious to trust to an experiment, the success of which was scarcely whithin the bounds of probablity; he amused his followers with prtended visions, which with the aid afterwards of the civil and military powr; and as the accomplishment of that event was by a few obscure persons, who founded their pretentions upon authority from heaven, we are next to consider, what kind of proofs of their divine commission they offered to the world; and whether they themselves could have been deceived, or mankind could have been deludded by them."

- Samuel Vince

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"A very eminent writer has observed, that "the conversion of the Gentile world, whether we consider the difficulties attending it, the opposition made to it, the wonderful work wrought to accomplish it, or the happy effects and consequences of it, may be considered as a more illustrious evidence of God's power, than even our Saviour's miracles of casting out devils, healing the sick, and raising the dead." Indeed, a miracle said to have been wrought without any attending circumstances to justify such an exertion of divine power, could not easily be rendered credible ; and our author's argument proves no more. If it were related, that about 1700 years ago, a man was raised from the dead, without its answering any other end than that of restoring him to life, Iconfess that no degree of evidence could induce me tobelieve it; but if the moral government of God appeared in that event, and there were circumstances attending it which could not be accounted for by any human means, the fact becomes credible. When two extraordinary events are thus connected, the proof of one established the truth of the other. Our author has reasoned upon the fact as standing alone, in which case it would not be easy to disprove some of his reasoning; but the fact should be considered in a moral view - as connected with the establishment of a pure religion, and it then becomes credible. In the proof of any circumstance, we must consider every principle which tends to establish it; whereas our author, by considering the case of a man said to have been raised from the dead, simpli in a physical point of view, without any reference to a moral end, endavours to show that it cannot be rendered credible; and, from such principles, we may admit his conclusions without affecting the credibility of Christianity. The general principle on which he establishes his argument, is not the great foundation upon which the evidence of Christianity rests. He says, "Notestimony can be sufficient to establish a miracle, unless it be of such a kind, that the falsehood would be more miraculous than the fact which it endavours to prove." Now this reasoning, at furthest, can only be admitted in those cases where the fact has nothing but testimony to establish it. But the proofs of Christianity do not rest simply upon the testimony of its first promulgators, and that of those who were affterwards the instruments of communicating it; but they rest principally upon the acknowledged and very extraordinary affects which were produced by the preaching of a few unlearned, obscure persons, who taught "Christ crucified;" and it is upon these indisuptable matters of ffact which we reason; and when the effects are totally unaccountable upon any principle which we can collect from the operation of human means, we must either admit miracles, or admit an effect without an adequate cause. Also, when the proof of any position depends upon arguments drawn from various sources, all concutring to establish its turh, to select some one circumstance, and atrempt to show that that alone is not sufficient to render the fact credible, and thence infer that it is not ture, is a conclusion not to be admitted. But it is thus that our author has endavoured to destroy the credibiliry of Christianity, the evidences of which depend upon a great variety of circumstances and facts which are indisputably true, all cooperating to confirm its truth; but an examination of these falls not whithin the plan here proposed. He rests all his arguments upon the extraordinary nature of the fact, considered alone by itself; for a common fact, with the same evidence, would immediately be admitted. I have endavoured to show, that the extraordinary nature, as much as the mosst common events are necessary to fulfill the usual dispensations of Providence, and therefore the Deity was then direted by the same motive as in a more ordinary case, that of affording us such assitance as our moral condition renders necessary. In the establishment of a pur religion, the proof of its divine origin may require some very extraordinary circumstances which may never afterwards be requisite, and accordingly we find that they have not happened. Here is therefore a perfect concistencty in the operation of the Deity, in his moral government, and not a violation of the laws of nature: Secondly, the fact is immediately connected with others which are indisputably true, and which, without the supossition of the truth of that fact, would be, at least, equally miraculous. Thus I conceive the reasoning of our author to be totally inconclusive; and the argumentss which have been employed to prove the fallacy of his conclusions, appear at the same time, fully to justify our belief in, and prove the moral certainty of, our holy religion."

- Samuel Vince

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"The book which Peckham wrote in the defence of his order against William of St. Amour was probably written before he became archbishop... but the unpopularity of the friars among the clergy had extended to England, and he was obliged to defend them... They are accused by one of our chroniclers of gaining a temporary shelter on the lands of an abbey, just to rest... then, hastily building a wooden altar and covering it with the consecrated stone they carried, they celebrated mass, and it was impossible to eject them. He complains too of their poaching... by hearing the confessions of those who were ashamed to confess to the parson whom they saw every day, or who scorned to do so because he was as vicious as themselves or were afraid of his blabbing their secrets when drunk. The clergy of England... attempted to stop this abuse... and asserted that it was an unlawful... In this they were technically wrong, for pope Martin IV... had confirmed... the power of committing to "friars of the said order... the office of preaching, of hearing confessions and absolving penitents..." with a strict prohibition of any interference. The pope, however, stipulated that the faithful must confess to their parish priest once a year. But this was not observed... for the theological faculty at the university of Paris in the same year gave it as their opinion that no one was bound to confess the same sins specifically to two persons. This would be, says Peckham, to straiten the way of eternal life which the Holy Father intended by this privilege to widen."

- John Peckham

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