Synopsis of Universal Geometry

...Snell the Dutchman, Viète the Frenchman, and others, the glory and ornament of this work, approach Provence to congratulate her that she has Louis de Valois, a Patron of men of letters, as her Governor.
original: "uinum Batavos; Victam Gallum." Mersenne is referring to Willebrord Snellius and François Viète. "Proregem" refers to Valois's role as the King's representative or Governor in Provence.

England, as if bearing it ill that those others preceded her in honoring You, proves through two works—with the most solid and exquisite demonstrations—that the last place among those leaders is by no means her due; therefore, armed with the brightest rays of light, she bows and lays her Refractions at your feet.
original: "Refractiones." This likely refers to the work of English scientists on optics and the behavior of light, which Mersenne included in his mathematical compendium.

May God, the Best and Greatest, grant that just as this truth is accustomed to rescue Geometers from false reasoning, so may the Eternal Truth—which you love so dearly—free us from all errors, both practical and speculative. May this continue until the riddles that dim the sharpness of our mind are solved, and you are bathed in its full light, and you may perpetually contemplate those Royal words,
original: "paralogismis." A paralogism is a piece of illogical or fallacious reasoning, specifically in a mathematical proof.

Blessed are they who dwell in your house, O Lord; they will praise you forever and ever. They will pour forth the memory of the abundance of your sweetness, and they will rejoice in your justice,
original: "Beati qui habitant... exultabunt." Mersenne quotes a combination of Psalm 84:4 and Psalm 145:7 from the Latin Vulgate Bible.

caught up in eternal glory.