Coincide Quotes (5 quotes)
Every investigator must before all things look upon himself as one who is summoned to serve on a jury. He has only to consider how far the statement of the case is complete and clearly set forth by the evidence. Then he draws his conclusion and gives his vote, whether it be that his opinion coincides with that of the foreman or not.
Having discovered by observation and comparison that certain objects agree in certain respects, we generalise the qualities in which they coincide,that is, from a certain number of individual instances we infer a general law; we perform an act of Induction. This induction is erroneously viewed as analytic; it is purely a synthetic process.
I have therefore tried to show the tendency displayed throughout history, by the most profound investigators, to pass from the world of the senses to a world where vision becomes spiritual, where principles are elaborated, and from which the explorer emerges with conceptions and conclusions, to be approved or rejected according as they coincide with sensible things.
We have very strong physical and chemical evidence for a large impact; this is the most firmly established part of the whole story. There is an unquestionable mass extinction at this time, and in the fossil groups for which we have the best record, the extinction coincides with the impact to a precision of a centimeter or better in the stratigraphic record. This exact coincidence in timing strongly argues for a causal relationship.
What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same propertythe screw. The right line, the circle, the screwthe representations of translation, rotation, and the two combinedought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.