A gallery chock-full of Botticellian lips and tits is no place to start disputing the central premise of this show, that the Florentine artist’s paintings are woven into the fabric of our collective visual consciousness. From tuppenny ha’penny statuettes to a Dolce & Gabbana trouser suit printed with fragments of the Birth of Venus, Botticelli’s most famous paintings, whether in spirit, pastiche or frank reproduction, are everywhere.

In Hell, the souls of the damned endure cruelly imaginative punishments for all eternity. Corrupt churchmen are buried headfirst in the ground with their feet set on fire, and soothsayers, who in life presumed to be able to see into the future, have their heads turned 180 degrees and are forced to walk around looking backwards. Drawn in metalpoint strengthened here and there with ink, Botticelli’s lines are as fine as spider’s silk. Sometimes barely there at all, their extraordinary refinement lends a strange, jarring intensity to the violence and terror they depict.

Waldemar Januszczak always has a provoking agenda to shape his now nearly countless forays into television art history. In this four-part series he's out to challenge what he sees as the unthinking acceptance of the one-dimensional traditional and monopolistic version of the Renaissance.

Now that Renaissance altarpieces live for the most part in museums and not churches, our experience of them is, quite literally, flat. Once, the winged altarpieces so popular in northern Europe, comprising a central panel flanked by two moveable “doors”, would have changed appearance according to the Church calendar, the wings left closed during Lent to be opened again at Easter when the glorious colours of its central image would once again be revealed.

Some time in the late 1280s, the artist Cimabue was wandering in the Tuscan countryside when he chanced upon a boy shepherd. According to Vasari, whose Lives of the Artists is the source for most such stories, the boy was “portraying a sheep from nature on a flat and polished slab, with the stone slightly pointed, without having learnt any method of doing this from others, but only from nature.” The young untrained artist was Giotto, who would be taken to Florence as Cimabue's apprentice and soon outstrip his master.

At first sight Piero della Francesca’s The Nativity appears to be a simple picture, especially when compared with more flamboyant depictions of the scene by artists such as Gentile de Fabriano, Botticelli and Rubens. Like a director staging a play on a limited budget, Piero has been sparing with his cast, props and scenery.

There’s a lot of breathless frontloading in television documentaries. The headlines promising shock and awe coming up are posted in the opening edit as a way of hooking in the remote-wielding viewer. Very often as presenters stump around history’s muddy digs or leaf through dusty old tomes, the revelations vouchsafed turn out to be a bit iffy, a bit yeah but no but so what? The hyperventilation is often a precursory guarantee of bathos. You’d be better off reading the book. So Andrew Graham-Dixon had to draw on an extra reserve of superlatives to sell Secrets of the Mona Lisa.

The strikingly architectural space that forms the upper portion of Botticini’s Palmieri altarpiece is well-suited to an entrance, forming as it does a sort of triumphal arch heralding great things beyond. And so it is that for years this painting hung over the entrance to the National Gallery’s Sainsbury Wing, oddly well-placed, but in truth of course, entirely out of place.

Unlike Venice, where colour reigned supreme among artists such as Titian and Veronese, Florence was the city where drawing – disegno – was held up as the cornerstone of the artist’s education. Think of the well-defined musculature of Michelangelo’s figures. Florentine artists of the Renaissance practiced an art of detailed precision, mastering clarity of line and structural rigour.

The young, rather homely yet grand gentleman is lounging under a tree, behind him a formal knot garden. His costume is extravagant and rich, and his hat is charming. This exquisite 1590s miniature by Isaac Oliver, watercolour on vellum, titled indeed A Young Man Seated Under a Tree, is the first depiction in art of a knot garden; flowers and plants by the tree are meticulously detailed, and in the background is the classic Renaissance knot garden.