and that when we come to work our way to the knowledge of things around us, from the sod on which we stand, to the most remote luminary in the heavens upon which two hundred millions of miles will tell as a measurable fraction, will readily admit, that mathematics is not only the line wherewithal to measure, and the balance wherein to weigh, but that it is the wedge to cleave asunder whatever is too gnarly and stubborn, and the lever to heave aside whatever is too weighty for the other apparatus of thinking and executing.

Those who have formed their notions from those nominal mathematicians, who idle with the disjointed bones of the science in the absence of the life, are apt to suppose, and sometimes to say, that mathematical science has a tendency to curb the fancy, and pedantify the mind. Among all the blunders of ignorance there is not one more gross than this; and we might appeal with triumph to mathematicians of every age as leaving recorded in their writings, abundant evidence of the most exalted and expanded imagination, and the most chaste and lively fancy. I shall mention only one or two names; and these of the last and the present generation. Who in his time excelled or even equalled the late John Playfair of Edinburgh, (with whom I have again and again discussed the subject and plan of this work,) in power, in purity, and in beauty of style? And who, in our own times, writes like Whewell or Herschel? Find me the unmathematical man that shall set an idea before the mind, as a mental and tangible solid, with the same power and truth as either of them,

and I shall abandon my argument, and join ever after “the herd of gentlemen who write with ease.”

So much for the plan and purpose of the work; and the execution can be best seen and judged of in the work itself; therefore I shall only state further that I have been careful to bring forward the three branches in such an order of succession, as that the reader who reads for instruction, (as I sincerely hope many will,) may call them all to his aid whenever he feels it necessary. I have dwelt longest upon those general points which appeared to me to possess in the highest degree the two qualities of furnishing the greatest number of inferential truths and stimulating the reader to seek out those truths; and I have been more anxious to create a love of the science, than to carry the particular departments of it to a great extent. To use a homely simile, if a man gets lamed before he commences a journey, it is far better to cure him and let him start in his own strength, than to carry him half way and leave him in his lameness. But this simile, homely though it is, applies to every branch of education, and to mathematics in an especial manner. To talk about teaching a person a science, is like talking about a lame man's performing a journey when he is carried; but, if we can succeed in awaking the desire and arousing the capacity, the party will learn, not only without our teaching, but in spite of our opposition; and this is the grand object which should be aimed at by every well-wisher to the mental and moral character of the human race.

I cannot say that I shall conclude this preface-for the

same train of thought is continued in the introduction— but I shall conclude the present writing by claiming the suffrages of the public in favour of my purpose, how much soever they may blame the execution of it,-only adding, that if the present volume shall meet with a reception at all proportionate to the labour it has cost me, I purpose following it up by another, carrying the three branches of the science as far as they are required by those who are not professional mathematicians.

Grove Cottage, Chelsea,

July, 1836.

ROBERT MUDIE.