"As to Cavalierian methods: one deceives oneself if one accepts their use as a demonstration, but they are useful as a means of discovery preceding a demonstration. ...Nevertheless, that which comes first and which matters most is the way in which the discovery has been made. It is this knowledge which gives most satisfaction and which one requires from the discoverers. It seems, therefore, preferable to supply the idea through which the result first came to light and through which it will be most readily understood. We will thereby save ourselves much labour and writing and the others the reading; it is necessary to bear in mind that mathematicians will never have enough time to read all the discoveries in Geometry (a quantity which is increasing day to day and seems likely in this scientific age to develop to enormous proportions) if they continue to be presented in a rigorous form, according to the manner of the ancients."