I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind. - René Descartes

I am, I exist” is necessarily true every time I utter it or conceive it in my mind.

"("I think, therefore I am"), the idea that the mere act of thinking about one's existence proves there is someone there to do the thinking."

punto de partida es la duda metódica. La duda cartesiana no es escepticismo, sino un procedimiento dialéctico de investigación, encaminado a desprender y aislar la primera verdad evidente, la primera idea clara y distinta, la primera naturaleza simple.

Thus, all unknown quantities can be expressed in terms of a single quantity, whenever the problem can be constructed by means of circles and straight lines, or by conic sections, or even by some other curve of degree not greater than the third or fourth.
But I shall not stop to explain this in more detail, because I should deprive you of the pleasure of mastering it yourself, as well as of the advantage of training your mind by working over it, which is in my opinion the principal benefit to be derived from this science. Because, I find nothing here so difficult that it cannot be worked out by anyone at all familiar with ordinary geometry and with algebra, who will consider carefully all that is set forth in this treatise.