Traupman treats
hora prima as 1:00.
Vaquero treats
hora prima as the hour between 12:00 and 1:00, so that
hora secunda is the hour between 1:00 and 2:00. This is the way time is expressed in some (but apparently not all) parts of Germany and in Russian (Viertel zwei = 1:15 in eastern Germany; see below), and for all I know the Spanish way, too. But Vaquero is a little confused on this point.
Est (hora) secunda et dodrans = cum dodrante = dempto quadrante
Vaquero apparently offers three alternatives:
1.
Est (hora) secunda et dodrans (
hora secunda = the second hour (i.e., 1:00) and three-quarters.
2.
Est (hora) secunda cum dodrante (
hora secunda = the second hour (i.e., 1:00), with three-quarters.
3.
Est (hora) secunda dempto dodrante. If the hour between 1:00 and 2:00 is treated as
hora secunda, it would be necessary to express 1: 45 as
hora tertia dempto quadrante, unless you are following Traupman's system.
I would like it to be "correct" Latin. When there are two different ways of using dodrans leading to different times, that is a problem, in my opinion.
Of course it's a problem. There haven't been any native speakers of Latin for 1,500 years, more or less, and native speakers of Latin didn't measure time uniform units and certainly didn't measure time in quarters of hours. Under the circumstances, what standard do you propose to look to in order to determine "correct" Latin?
The alternatives offered by Traupman and Vaquero are simply made up our of thin air to express an un-Latin concept in a blind guess as to what an ancient Roman might say if he or she had a timekeeper that measured uniform hours and had a minute hand, in order to express in Latin concepts that didn't enter common currency in European languages until the mid-19th century. They're no different than a textbook on number theory in Pirahã. In other words, each of the proposed expressions for 1:45 is equally valid. Take your choice.
From the Wikipedia article "Uhrzeit":
Je nach Region sind unterschiedliche Aussprachen gängig. So wird 17:15 Uhr im Westen Deutschlands, d. h. genauer westlich der Linie Lübeck–Saarbrücken, sowie in Teilen Bayerns und Baden-Württembergs, in der Schweiz, in Liechtenstein und in Vorarlberg gewöhnlich als „Viertel nach fünf“ bezeichnet (in Teilen Österreichs auch „Viertel über fünf“ und in der Schweiz auch „Viertel ab fünf“). Östlich der Linie wird von „viertel sechs“ gesprochen. Analog ist es bei der Bezeichnung von 17:45 Uhr, wobei im Westen „Viertel vor sechs“ und östlich dieser Linie sowie in Österreich „dreiviertel sechs“ üblich ist.