"These Exponents they call Logarithms, which are Artificial Numbers, so answering to the Natural Numbers, as that the addition and Subtraction of these, answers to the Multiplication and Division of the Natural Numbers. By this means, the Work of Multiplication and Division is performed by Addition and Subtraction; and consequently that of Squaring and Cubing, by Duplication and Triplication; and that of Extracting the Square and Cubic Root, by Bisection and Trisection; and the like in the higher Powers."

“In the year 1660 being importuned by some friends of his, I undertook so to teach Mr. Daniel Whalley of Northampton, who had been Deaf and Dumb from a Child. I began the work in 1661, and in little more than a year's time, I had taught him to pronounce distinctly any words, so as I directed him... and in good measure to understand a Language and express his own mind in writing; And he had in that time read over to me distinctly the English Bible; and did pretty well understand the Historical part of it. In the year 1662 I did the like for Mr. Alexander Popham... I have since that time taught divers Persons to speak plain and distinctly, who did before hesitate and stutter very much; and others, to pronounce such words or letters, as before they thought impossible for them to do: by teaching them how to rectify such mistakes in the formation, as by some natural impediment, or acquired Custome, they had been subject to.”

“This method of mine takes its beginnings where Cavalieri ends his Method of indivisibles. ...for as his was the Geometry of indivisibles, so I have chosen to call my method the Arithmetic of infinitesimals.”

“scarce looked upon as Academical studies but rather Mechanical... And among more than two hundred students in our college, I do not know of any two who had more of Mathematicks than I, which was then but little; and but very few, in that whole university. For the study of Mathematicks was at that time more cultivated in London than in the universities.”

“I saw, there was little or no Help to bee exspected from others; but that if I should have further Occasions of that Kind, I must trust to my owne Industry, and such Observations as the present Case should afford. And indeed the Nature of the Thing is scarce capable of any other Directions; every new Cipher allmost being contrived in a new Way, which doth not admit any constant Method for the finding of it out: But hee that will do any Thing in it, must first furnish himself with Patience and Sagacity, as well as hee may, and then Consilium in arenâ capere, and make the best Conjectures hee can, till hee shall happen upon something that hee may conclude for Truth.”

“At Christmass 1631, I was, for about a fortnight, at home with my Mother at Ashford. I there found that a younger Brother of mine had, for about 3 Months, been learning to Write and Cipher, or Cast account, When I had been there a few days; I was inquisitive to know what it was, they so called. And my Brother did shew me what he had been Learning in those 3 Months. Which was the Practical part of Common Arithmetick in Numeration, Addition, Substraction, Multiplication, Division, The Rule of Three the Rule of Fellowship the Pule of False-Position, Rules of Practise and Reduction of Coins, and some other little things. Which when he had shewed me by steps, in the same method that he had learned them; and I had wrought over all the Examples which he before had done in his book; I found no difficulty to understand it, and I was very well pleased with it: and thought it ten days or a fortnight well spent. This was my first insight into Mathematicks; and all the Teaching I had.”

“On March 4. 1644, 5. I married Susanna daughter of John and Rachel Glyde of Northjam in Sussex; born there about the end of January 1621, 2. and baptised Feb. 3 following. By whom I have a Son and two Daughters now surviving; John born Dec. 26 1650. Anne born June 4. 1656. and Elizabeth born Sept. 23 1658. ...My Wife died at Oxford Mar. 17. 1686, 7. after we had been married more than 42 years.”