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The quotes in question can be found in Macartney's Journal of an Embassy from the King of Great Britain to the Emperor of China. This journal was later (re?)published in Some account of the public life, and a selection from the unpublished writings, of the Earl of Macartney, Volume 2, which is available via archive.org.
The first quote can be found on p. 412–413. In this context, Macartney is discussing the attitude of Chinese leaders to the outside world, and hypothesizing that it may stem from the fact that they were more civilized than the rest of the world at one time.
When Marco Polo, the Venetian, visited China in the thirteenth century, it was about the time of the conquest of China by the western or Mongol Tartars, with Kublai-khan, a grandson of Gengis-khan, at their head. A little before that period the Chinese had reached their highest pitch of civilization; and no doubt they were then a very civilized people in comparison of their Tartar conquerors, and their European contemporaries; but not having improved and advanced forward, or having rather gone back, at least for these hundred and fifty years past, since the last conquest by the northern or Mantchou Tartars, whilst we have been every day rising in arts and sciences, they are actually become a semi-barbarous people in comparison with the present nations of Europe. Hence it is that they retain the vanity, conceit, and pretensions that are usually the concomitants of half-knowledge; and that, though during their intercourse with the embassy, they perceived many of the advantages we had over them, they seemed rather surprised than mortified, and sometimes affected not to see what they could not avoid feeling. In their address to strangers they are not restrained by any bashfulness or mauvaise honte [“false modesty”–ed.], but present themselves with an easy confident air, as if they considered themselves the superiors, and that nothing in their manners or appearance could be found defective or inaccurate.
The second quote can be found on p. 398. In this passage, Macartney is discussing the possible consequences of an armed conflict between England and China, and how it would (among other things) disrupt the British economy. He then notes that internal misfortune in China might also lead to a trade disruption, likening China to a warship.
But all these inconveniences and mischiefs, which I have stated as objects of apprehension, may happen in the common course of things without any quarrel or interference on our part. The empire of China is an old crazy first-rate man of war, which a fortunate succession of able and vigilant officers has contrived to keep afloat for these hundred and fifty years past; and to overawe their neighbors, merely by her bulk and appearance; but whenever an insufficient man happens to have the command upon deck, adieu to the discipline and safety of the ship. She may perhaps not sink outright; she may drift some time as a wreck, and will then be dashed in pieces on the shore; but she can never be rebuilt on the old bottom.
Note that the word "crazy" in this quote does not mean "insane" as it frequently does today, but instead is an older sense of the word meaning "full of cracks or flaws; damaged, impaired, unsound; liable to break or fall to pieces; frail, 'shaky'" (OED). Similarly, "first-rate" in the context of a warship means a particularly large warship (hat tip to @Jan for pointing this out in the comments.)