[6] +das Lot (Loth)+: plumb-line. [7] +Vielfache+: multiples. [8] +giebt ... an (angeben)+: states. [9] +Pyknometer+: specific gravity flask. [10] +Es sei nun P_{1} das Gewicht+: now let P_{1} be the weight. [11] +alsdann = dann+: then. [12] +einer ... Marke+; see 1 Note 10. 13. [1] +Orte und Lagen+: places and positions. [2] see 1 Note 2. [3] +gelegen+: situated. [4] +fortschreitende Bewegung+: motion of translation. [5] +die ... Wege+: the paths; see 1 Note 10. [6] +von einem ... begriffenen Körper+: of a body engaged; see 1 Note 10. [7] see 1 Note 2. [8] +der ... Weg+: the path; see 1 Note 10 [9] +infolge (in Folge)+: in consequence. [10] +einer beliebig+: of any desired, of any whatever. [11] +kommt ... zu stande+: comes about, is brought about. [12] +bei+: in the case of (not _by_.) +Bei+ is of very common occurence with this meaning, which will generally suggest the proper preposition (at, with, in etc.) to use in English. 14. [1] +die Gewichtseinheit+: unit of weight. [2] +heisst+: means. [3] +die Breite+: latitude. [4] +am Meeresspiegel+: at the level of the sea. [5] +am bequemsten+: most conveniently. [6] +darstellen+: to represent. [7] +t+ stands for +Tonne+ = 1000 kg. [8] see 1 Note 2. [9] Observe that the comma is used as a decimal point and the period as a sign of multiplication. [10] +also+; see 2 Note 2. [11] +nimmt ... zu (zunehmen)+: increases. [12] see 1 Note 2. [13] +um+: to the distance of. [14] +die Gesammtarbeit+: total work. [15] +einzel (einzeln)+: separate. 15. [1] See 1 Note 2. [2] +aufgespeichert+: stored up. [3] +bei Verminderung+: on diminishing; see 13 Note 12. [4] +um+: to the distance of. [5] +musste+: had to. Do not translate by _must_; it is in the past tense. [6] +geleistet: (leisten)+: performed. +Die Leistung+: performance. [7] +streng genommen+: taken strictly = strictly speaking. [8] +eine Feder spannen+: compress a spring. [9] +die Spannkraft+: tension, potential. [10] +bei Beurtheilung+: in judging; see 13 Note 12. [11] +ist massgebend+: is decisive, is a criterion. [12] +hinsichtlich+: as regards. [13] +u. s. f. (und so fort)+: and so forth. 16. [1] +Nebenformen+: secondary forms. [2] +noch so komplizierten+: never so complicated, no matter how complicated. [3] +rollen+: the hyphen indicates that +hinab+ belongs also to +rollen+: to roll down. [4] +stellt ... dar (darstellen)+: represents. [5] +einen ... Druck+; see 1 Note 10. [6] +aufheben+: to neutralize, balance. [7] +der Fall+: case. [8] +aufzufassen+: to conceive. [9] +entstanden (entstehen)+: originated, formed. [10] +flachgängig+: square-threaded. [11] +bez. (beziehungsweise)+: or as the case may be. [12] +scharfgängig+: v-threaded. [13] +der Schraubengang+: turn of the screw. [14] +das Gewinde+: thread. [15] +die Bolzenstärke+: thickness of the cylinder. +Stärke+, usually strength, also means thickness. [16] +die Kernstärke+: thickness, of the core.