From the book
Hipparchus
Plato · Diotimos Editions · 2026
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At a Glance
- The wordΣταθμός means weight, here a weight or amount measured by weighing.
- In HipparchusThe exchange at 231d tests the revised proposal that less expenditure followed by more acquisition is gain.
- In this editionThe apparatus reports διστάσιον from T against B’s διστάσιμον; Burnet prints the former.
- A place to readχρυσίου σταθμὸν ἥμισυν — The outlay is expressed as half a weight of gold.
Meaning
Σταθμός means weight, here a weight or amount measured by weighing. Ἥμισυς means half; διπλάσιος means double or twice as much. Δωδεκαστάσιος means twelve times the weight, and διστάσιος twice the weight. Ἀντί means in place of or in exchange for. The printed forms include σταθμὸν ἥμισυν, “half a weight,” διπλάσιον, “double,” and the comparison ἀντὶ δωδεκαστασίου ... διστάσιον.
These expressions must be distinguished from ἀξία, worth. Weight measures a physical quantity, while the argument asks whether receiving more weight increases what the possessor has in value. “Exchange” describes the hypothetical giving and receiving; the text supplies no separate technical noun for an exchange market.
Use in the book
The exchange at 231d tests the revised proposal that less expenditure followed by more acquisition is gain. The metals differ, so counting or weighing without valuing is insufficient. The companion accepts that a greater silver receipt can be a loss when compared with the gold surrendered. This is the passage’s secure argumentative result, independent of a complete reconstruction of its units.
The printed English asks about spending “half a weight of gold” and receiving “twice that weight of silver.” The answer says the gold becomes twice its weight instead of twelve times its weight. The edition’s note explains this as half a gold unit, worth six silver units, exchanged for one silver unit. That model takes the silver receipt as twice the gold actually given. Socrates’ next question is printed “is the double not more than the half?” The abbreviated comparison does not repeat the baseline for each term.
A reading that instead assigns half and double to one common unstated unit would produce a silver receipt of two units for gold worth six. It would still be a loss. This alternative is useful for showing why the main inference does not depend on choosing one reconstruction; it should not be substituted into the translation as though the edition had printed it. Neither the source nor this lexicon supplies grounds to declare textual corruption or a certain arithmetical blunder merely because the compressed expressions are difficult.
The transition after the example is more consequential than the arithmetic: worth must belong to gain. Even a formally correct inequality of weights would not establish an inequality of value between different metals. The companion’s “not in worth” explicitly names the missing respect of comparison. The small-and-great conclusion at 231e then detaches gainfulness from size in either direction.
The twelvefold ratio belongs to this argument and its explanatory note. The supplied comparison with Herodotus’ thirteen-to-one reckoning is a warning against turning the example into a universal historical price schedule.
Places to read
- 231dχρυσίου σταθμὸν ἥμισυν — The outlay is expressed as half a weight of gold.
- 231dἀντὶ δωδεκαστασίου — The expected twelvefold relation is contrasted with the actual receipt.
- 231dδιστάσιον αὐτῷ καθίσταται τὸ χρυσίον — The companion describes the inferior exchange result.
- 231dτὸ διπλάσιον τοῦ ἡμίσεος — The double and half are compared without restating all reference quantities.
Translation in this edition
The apparatus reports διστάσιον from T against B’s διστάσιμον; Burnet prints the former. That recorded variation does not itself resolve the reference units. The edition follows Burnet and supplies note 22’s model. This article keeps text, translation, explanatory model and interpretive caution distinct rather than giving a silently repaired quotation.