How we cite our quotes: (Chapter.Section.Paragraph) or (Chapter.Paragraph)
Quote #1
In general, the greater the productivity of labor, the less the labour-time required to produce an article, the less the mass of labour crystallized in that article, and the less its value. Inversely, the less the productivity of labour, the greater the labour-time necessary to produce an article, and the greater its value. (1.1.17)
Advances in technology often increase productivity. Increased productivity means that the production of commodities doesn't take as long, so value of those commodities goes down. So, advances in technology generally make goods and services cheaper.
Quote #2
The circulation of commodities is the starting-point of capital. The production of commodities and their circulation in its developed form, namely trade, form the historic presuppositions under which capital arises. World trade and the world market date from the sixteenth century, and from then on the modern history of capital starts to unfold. (4.1)
The origin of the modern mode of production, capitalism, dates back to the 16th century. That's when the economic system we know today started to unfold out of feudalism, the previous system in Europe. Might there be another mode of production someday?
Quote #3
The historical conditions of [capital's] existence are by no means given with the mere circulation of money and commodities. It arises only when the owner of the means of production and subsistence finds the free worker available, on the market, as the seller of his own labour-power. And this one historical pre-condition comprises a world's history. Capital, therefore, announces from the outset a new epoch in the process of social production. (6.9)
Marx says there's a crucial variable that allowed the modern mode of production, capitalism, to emerge. That's the emergence of free workers: people who can sell their labor-power—as opposed to, say, serfs or slaves.